# Consumer-side Fairness in Recommender Systems: A Systematic Survey of
Methods and Evaluation

Bjørnar Vassøy and Helge Langseth
Norwegian University of Science and Technology

###### Abstract

In the current landscape of ever-increasing levels of digitalization, we are
facing major challenges pertaining to scalability. Recommender systems have
become irreplaceable both for helping users navigate the increasing amounts of
data and, conversely, aiding providers in marketing products to interested
users. The growing awareness of discrimination in machine learning methods has
recently motivated both academia and industry to research how fairness can be
ensured in recommender systems. For recommender systems, such issues are well
exemplified by occupation recommendation, where biases in historical data may
lead to recommender systems relating one gender to lower wages or to the
propagation of stereotypes. In particular, consumer-side fairness, which
focuses on mitigating discrimination experienced by users of recommender
systems, has seen a vast number of diverse approaches for addressing different
types of discrimination. The nature of said discrimination depends on the
setting and the applied fairness interpretation, of which there are many
variations. This survey serves as a systematic overview and discussion of the
current research on consumer-side fairness in recommender systems. To that
end, a novel taxonomy based on high-level fairness interpretation is proposed
and used to categorize the research and their proposed fairness evaluation
metrics. Finally, we highlight some suggestions for the future direction of
the field.

##  1 Introduction

Recommender systems have become integral parts of modern digital society. An
exponential increase in data poses significant challenges to users and
consumers, who cannot feasibly sift through everything to find what they are
looking for. Recommender systems help mitigate these challenges by capturing
their users’ preferences and presenting them with prioritized options. Thus,
recommender systems have seen widespread application in e-commerce, multimedia
platforms, and social networks. Their tactical relevance in the industry has
led to a high degree of cooperation between the industry and academia in
further developing the field.

In recent years, the notion of fairness in machine learning has steadily
gained attention. High-profile cases have succeeded in bringing the topic to
the general public’s attention, like the analysis performed by ProPublica
suggesting the presence of racial bias in the COMPAS system used for
predicting the likelihood of recidivism of inmates (ProPublica, 2016).
Subsequently, fairness challenges have also been identified for recommender
systems, and the works of Burke (2017) formalized the presence of multi-
stakeholder fairness dynamics mirroring the multi-stakeholder nature of
recommender systems. Provider stakeholders may take issue if their products
are disproportionally less exposed than similar popular products. Career
seekers may feel discriminated against if they are predominantly recommended
careers that are stereotypically and historically associated with their
gender. An increased focus on fairness in recommender systems is not only
ethically beneficial for society as a whole but also helps the actors applying
them in satisfying an increasingly fairness-aware user base and retaining good
relations and cooperation with providers.

While provider-side fairness research has a dominant subgroup in research
pursuing popularity bias, which is the notion of disproportional amounts of
attention given to popular items, consumer-side fairness research has a
greater focus on group-based fairness relating to demographic information of
the users, i.e., making sure that users are not discriminated against based on
aspects such as race, gender, or age. Despite the focus on a specific high-
level fairness setting, consumer-side fairness in recommender systems displays
a high degree of variation in approaches. The approaches for introducing
fairness awareness take place in all parts of the recommender system pipeline,
span most established and upcoming model architectures, and are designed for
respecting various fairness interpretations. Some models opt for adjusting
recommendations post hoc, others modify the input data directly, while others
still explicitly model the fairness-awareness. Fairness has been incorporated
through penalizing discrimination during optimization, altering user
representation to be more neutral, probabilistically modelling the influence
of sensitive attributes, or re-ranking unaltered recommendation, all while
adhering to different definitions of what discrimination and fairness entails.
There is also variation in the application setting of these approaches; most
adhere to the regular asymmetric setting where users and items make up
fundamentally different concepts, while others consider reciprocal settings
where users are recommended to other users like matchmaking. Yet another
dynamic is considered in two-sided settings that seek to achieve both
consumer- and provider-side fairness concurrently. Despite the great variety,
the breadth of consumer-side fairness approaches has yet to be covered in
detail by any existing surveys. We further argue for this claim in Section
2.5, where we discuss relevant surveys.

In this survey, we have systematically surveyed the existing literature that
proposes and evaluates approaches considering consumer-side fairness. Critical
aspects of the qualified literature are discussed, compared, and categorized,
leading to the proposal of a taxonomy that highlights fairness interpretation
and how it has been incorporated into the approaches. Further, we provide a
comprehensive overview of metrics used to evaluate the fairness of the
approaches and some thoughts on the field’s future directions. Our key
contributions are:

  1. 1.

Propose a taxonomy for categorizing consumer-side fairness approaches in
recommender systems based on how the fairness is incorporated and high-level
conceptual fairness definitions.

  2. 2.

Provide a comprehensive overview, categorization, and comparison of available
consumer-side fairness approaches in recommender systems and their proposed
fairness evaluation.

The remaining sections of this survey include a background section on fairness
definitions, terminology, related concepts, and related works; methodology
covering the literature selection process and the proposed taxonomy; a
detailed discussion and comparison of the identified literature; analysis of
applied fairness metrics and datasets; and a final discussion of our thoughts
on the future directions of the topic.

##  2 Background

As a primer to this survey’s core content and discussion, we introduce key
established fairness concepts and terms that appear frequently or are subject
to ambiguity. The background also covers a discussion of recommender systems
concepts related to consumer-side fairness and a look into existing surveys on
fairness in recommender systems and how this survey differs.

###  2.1 Terminology

The following definitions have been added to mitigate confusion stemming from
mixing similar terms or different interpretations of specific terms. A low
degree of consensus, especially within fairness-focused research, has led to
multiple different terms being used for the same concept and other words like
preference are contextually ambiguous.

Rating: In rating-based recommender systems, we are interested in the rating
given by a specific user to a specific item and is contrasted with ranking-
based recommender systems. Ratings can be discrete and continuous and
typically have a set range, e.g., between 1 and 5.

Ranking: Ordering of items or entities according to users’ (perceived)
preference.

IR Ranking: The field of Information Retrieval comprise an array of different
approaches for retrieving information from data storage. We will consider
intent the key factor separating IR Ranking and recommender systems:
recommender systems seek to suggest novel, but relevant, information to their
users while IR Ranking seeks to retrieve the most relevant information.
Furthermore, IR Ranking approaches often involve a query and are rarely
personalized.

Top-$k$: Top $k$ ranked item, where $k$ is an integer indicating the number of
items that are of interest. $k$ is usually quite small, often in the range of
5-20, as user attention is a limiting factor.

Preference (score): Continuous measure of user preference used to produce
rankings.
Score/value/measure may be omitted in the text if the context allows it.

Ranking-based recommender systems: Recommender systems that learn to rank in
order to present the user with the top list of suggested items. Usually
applies classification-based optimization.

Rating-based recommender systems: Recommender systems that attempt to match
ratings given to items by users, and predict new ratings given by users to
unrated items. Usually applies regression-based optimization.

Sensitive attribute: Unifying term used to describe demographic attributes
that are used to segment users into different groups for which fairness
considerations are applied. Similar concepts, both symmetric and asymmetric,
have been referred to as demographic, protected, minority, marginalized and
private in the selected studies. Sensitive attribute is found to be sufficient
for explaining most approaches, but more thorough explanations are provided in
cases where asymmetry or special dynamics of a sensitive attribute take a more
nuanced role.

Sensitive group: A group of users that share a specific instance of a
sensitive attribute, e.g., all male users in a setting where gender is
considered a sensitive attribute.

###  2.2 Recommender System Definition

Table 1: Notation Symbols |  Description
---|---
$\mathcal{U}$ |  Set of all users
$\mathcal{V}$ |  Set of all items/recommendable entities
$\mathcal{S}$ |  Set of all possible sensitive attribute configurations
$r$ |  Rating in rating-based recommender systems. Double as preference in mixed usage
pref |  Intermediate measure of preference used in ranking-based recommender systems
$y$ |  Binary indicator for the presence of recommendation in ranking-based recommender systems
$\hat{}$ |  Modifier, indicate predicted output as opposed to ground truth
u,v,s |  Indicate relation with specific users, items or sensitive values respectively
Rec |  Set of (top-$k$) recommendations
$\text{Util}(\cdot)$ |  Open-ended/arbitrary utility function
$\text{P}(\cdot)$ |  Probability
$\hat{\mathbb{E}}[\cdot]$ |  Arithmetic Mean

Recommender systems comprise many varied approaches designed for varied
settings and present no clear singular definition. We will focus on
personalized recommender systems, i.e., those that seek to accommodate
different individuals with customized recommendations based on their
individual preferences. As alluded to in Section 2.1, this survey will
distinguish between rating-based and ranking-based recommender systems. When
applying the notation presented in Table 1, both flavours attempt to capture
how a set of entities $\mathcal{U}$ will value another set of entities
$\mathcal{V}$ on an individual level. $\mathcal{U}$ are typically exemplified
as users and $\mathcal{V}$ as items, and the overall goal is to recommend
novel items to the users. For rating-based recommender systems, the level
objective is to predict individual ratings given by a user $u$ to an item $v$,
$r_{uv}$, i.e., $\hat{r}_{uv}=r_{uv}$. Ranking-based recommender systems
instead take the approach of capturing the general preferences of the users
and using this to present the same users with selections of items predicted to
be of the users’ liking. The resulting objective is analogous to the rating-
based objective, $\hat{y}_{uv}=y_{uv}$, but does present slightly different
challenges owing to the non-continuous nature of ranking. Both Rating-based
and Ranking-based recommender systems may adapt rating data, but Ranking-based
recommender systems can more easily adapt data of a more implicit nature,
e.g., interaction events.

Recommender systems are implemented using a plethora of different models and
methods like Neighbourhood-based Collaborative Filtering (Nikolakopoulos et
al, 2022), Matrix Factorization (Koren et al, 2022), various types of Deep
Neural Networks (Zhang et al, 2022), Autoencoders (Li and She, 2017),
Reinforcement Learning (Afsar et al, 2021), Graph-based models (Wang et al,
2021), and various Probabilistic models. Detailed background theories of
various models have been left out to avoid significant inflation of the
survey’s length. However, as this is a comprehensive survey focusing on
tangible model proposals, some technical details will be discussed. Readers
are encouraged to consult auxiliary sources, like the provided references,
when needed.

###  2.3 Formal Fairness Definitions

Several formal fairness definitions have been proposed for classification
settings. While some of these can be trivially adapted to the recommendation
setting, others are more challenging. One such challenge relates to
adaptations of definitions based on confusion matrix statistics, as the
interpretations and implications of these statistics may differ between
classification and recommender systems. Confusion matrixes are not computable
nor relevant for rating-based recommender systems. Conversely, the confusion
matrixes of ranking-based recommender systems are heavily influenced by the
fixed number of recommendations and the number of correct recommendations,
which usually vary by user. Furthermore, the implications of some definitions
may be enhanced in scenarios where a positive label is deemed a positive
outcome for a stakeholder, even if it was a False Positive. An example of this
could be an applicant applying for a loan; the applicant will be happy if the
application is accepted regardless of whether it was the correct verdict
according to bank policies. In consumer-side recommendation settings, this is
rarely true, in which case, a False Positive in a top-$k$ recommendation
setting will simply be the presence of an item that the user does not care for
among the top recommendations.

A selection of fairness definitions is covered here, along with accompanying
descriptions of recommender system-specific adaptions. The reader is
encouraged to consult Gajane (2017), Caton and Haas (2020), and Li et al
(2022c) for a more in-depth discussion of formal fairness definitions in both
machine learning and recommender systems.

####  2.3.1 Fairness Through Unawareness

One of the more naive fairness definitions is achieved by simply omitting
explicit sensitive attributes in the modelling. This definition is widely
disregarded as it fails to consider implicit biases present in other
attributes and is therefore not sufficient for mitigating discrimination
(Gajane, 2017).

####  2.3.2 Statistical Parity

Statistical parity in classification requires that each group has an equal
probability of being assigned a positive label.

$\text{P}(\hat{y}=1\arrowvert s=s_{1})=\text{P}(\hat{y}=1\arrowvert
s=s_{2})=...$

Where $\text{P}(\cdot)$ represents probability, $\hat{y}$ is the predicted
label, and $s$ is a sensitive attribute.

Statistical Parity is adaptable in recommender systems by replacing the notion
of classification labels with ratings or discrete recommended items, but its
evaluation may be trickier.

####  2.3.3 Equal Opportunity

Equal opportunity in classification requires that the true positive rate of
different sensitive groups is equal.

$\text{P}(\hat{y}=1\arrowvert y=1,s=s_{1})=\text{P}(\hat{y}=1\arrowvert
y=1,s=s_{2})=...$

####  2.3.4 Equalized Odds

The Equalized Odds definition is stricter than Equal Opportunity in also
requiring that the false positive rates of the different sensitive groups are
equal.

$\displaystyle\text{P}(\hat{y}=1\arrowvert
y=1,s=s_{1})=\text{P}(\hat{y}=1\arrowvert y=1,s=s_{2})=...$ $\displaystyle\&\
$ $\displaystyle\text{P}(\hat{y}=1\arrowvert
y=0,s=s_{1})=\text{P}(\hat{y}=1\arrowvert y=0,s=s_{2})=...$

As previously mentioned, false positives may benefit some stakeholders in
certain scenarios. However, false positives may also be the most detrimental
type of error in other scenarios. Thus, the decision to pursue Equalized Odds
instead of Equal Opportunity may be motivated by a wish to balance either a
boon or a bane.

###  2.4 Related Recommender System Concepts

Many flavours of recommender systems have arisen to cover different needs as
they appeared or were made known. It is not uncommon that the concepts
considered in these different flavours partly overlap, share underlying
issues, or share similar mitigation strategies. A number of the most relevant
recommender system flavours, when compared with consumer-side fairness, are
listed in this section, focusing on similarities and dissimilarities. The
intention of this section is two-fold: The first is to highlight related
topics that may be of interest to readers and that may help put consumer-side
fairness into a broader context. The second motive is to highlight
dissimilarities that disqualify certain research from being covered by the
scope of this survey, despite occasionally adopting fairness terminology.

####  2.4.1 Provider-side fairness

As the name entails, provider-side fairness takes a polar opposite view to
consumer-side fairness. A significant part of the research focuses on
mitigating popularity bias, which occurs when popular items are given
disproportional amounts of exposure by the recommender system. However, the
broadness of the definition also covers research that is more similar to many
consumer-side fairness approaches in considering fairness for groupings based
on sensitive information from a provider perspective.

####  2.4.2 Cold-start, Long-tail and Diversity

Cold-start, long-tail, and diversity in recommender systems all make out
similar concepts with partly overlapping causes and mitigation approaches:
Cold-start specifically focuses on the scenario of providing good
recommendations for new users or new items, through facing the challenge of
comparatively little data for the new entity. Long-tail recommender system
approaches more generally attempt to improve the recommendation of items that
have few interactions compared to the more popular items or the analogous
user-centric alternative in improving the recommendations for inactive users.
Approaches that optimize for Diversity attempt to diversify the top-$k$
recommendations given to users, motivated by popularity bias issues and an
effort to enhance the user experience. While the definitions differ in
generality and perspective, they are sometimes used interchangeably in the
literature, especially cold-start and long-tail. Provider-centric approaches
of all three fields share similarities, or directly overlap, with popularity
bias mitigation approaches proposed as provider-side fairness-focused
recommenders. Similarly, user-centric approaches that seek to balance the
performance of all individual users may overlap with consumer-side fairness
approaches and are included in this survey, given that they satisfy all
acceptance criteria. The last point typically boils down to whether a fairness
perspective is applied, i.e., posed as individual fairness, along with
fairness evaluation. However, as a general strategy, research that seeks to
balance the utility of user groups based on number of user interactions have
been excluded because they fit perfectly within the mature fields of cold-
start or long-tail recommender systems, and are better represented when
compared with such methods.

####  2.4.3 IR Ranking Fairness

IR Ranking is typically not personalized, i.e., the produced rankings are not
affected by user-specific interaction with the system. Subsequently, IR
Ranking fairness objectives usually have a provider-side point of view, e.g.,
balancing the exposure achieved by similar items or the representation of
different item groups given non-personalized queries. The work of Pitoura et
al (2022) provides an overview of fairness in the IR Ranking setting.

####  2.4.4 Group Recommendation

Group recommendation approaches seek to recommend a set of items to a
collection of users, e.g., recommending a travel destination for a group of
friends with different preferences. This field frequently applies the term
fairness when explaining their motive of balancing the consideration of the
various users in the groups, and most consumer-side fairness concepts covered
in this survey are applicable within the groups or aggregated over groupings.
However, because the field is specialized for a specific recommender system
scenario and has received significant attention both before and after the
notion of fairness gained traction, these approaches are not included in this
survey.

####  2.4.5 Privacy

Privacy in recommender systems covers many approaches that seek to protect
privacy in different stages of the recommender system pipeline. For instance,
federated learning can be applied to mitigate the issues of having a
centralized model that may be breached and mined for sensitive information (Li
et al, 2020). Differential privacy has been applied to provide protection
guarantees for the sensitive information of individual users (Friedman and
Schuster, 2010). Some privacy approaches seek to completely remove the
information of specific attributes within user representations or data, which
overlaps with a class of fairness approaches that do the same with the
intention of not having the attributes influence the recommendation.

###  2.5 Related Work

There has been a recent surge in proposed surveys of fairness in recommender
systems. Pitoura et al (2022) surveys both fairness in IR ranking and
recommender systems, while Deldjoo et al (2023); Wang et al (2022); Li et al
(2022c) focus on recommender systems. Pitoura et al (2022) seeks to serve as
an overview of fairness in both IR ranking and recommender systems, which
makes it the broadest and most high-level survey among the ones considered
relevant. They propose using multiple established concepts as a basis for
their categorization, e.g., individual/group fairness and provider/consumer
side fairness, as well as novel classifications of fairness incorporation
methods. Because of the broad scope and since it is the oldest survey
considered relevant, only two of the studies covered in this survey were
covered in Pitoura et al (2022).

Deldjoo et al (2023); Wang et al (2022); Li et al (2022c) were all first made
publicly available within a few months of each other in 2022 and all consider
a broad scope comprising all types of fairness in recommender systems. This
scope is wider than the one applied in this survey by covering provider-side
fairness and group recommendation. Additionally, all three surveys also cover
research that is theoretical in nature or performs analysis using established
approaches and datasets, i.e., not necessarily proposing new models or
methods. Deldjoo et al (2023) investigate the current state of fairness in
recommender systems, and focus on charting how the available research is
distributed with respect to different high-level concepts. They additionally
propose a single-level categorization of the fairness metrics considered in
the research they cover. Li et al (2022c) has a more conceptual take and
provides a thorough introduction to fairness theory and fairness in other
machine learning fields before addressing their identified research through
multiple different taxonomies based on binary concepts. Some of the fairness
concepts they use to categorize the research are well established, like
group/individual and consumer/provider, while others have not previously been
focused on, like short-term/long-term and black box/explainable. Wang et al
(2022) propose a hierarchical taxonomy of fairness definitions that are since
used to categorize the optimization and fairness metrics applied in their
identified studies.

Our work differs from previous surveys by specializing in tangible solutions
proposed for consumer-side fairness in recommender systems. The specialization
allows for a complete overview of the available literature and a higher focus
on technical aspects to enhance comparisons. We also categorize our identified
research using a new taxonomy centred on high-level notions of fairness
interpretations and incorporation methods, which has a purposely high-level
and general definition to be applicable and extendable to new fairness
interpretations and incorporation methods. The completeness of our survey is
exemplified by Table 2, which indicates that when adjusting for time, the
largest coverage overlap with the broader surveys only comprises 18 out of the
43 articles we identified in the same time interval.

Table 2: Table displaying the coverage in the most relevant surveys of the articles identified in this survey. Raw counts and percentages are presented, both adjusted and unadjusted for the publish date of the last considered article in each survey. | Adj. Coverage | % Adj. Coverage | Tot. Coverage | % Tot. Coverage
---|---|---|---|---
Deldjoo et al (2023) | 14/43 | 33% | 14/47 | 30%
Li et al (2022c) | 18/43 | 42% | 18/47 | 38%
Wang et al (2022) | 16/41 | 39% | 16/47 | 34%

##  3 Methodology

The methodology of this survey covers the systematic selection process applied
for identifying and screening relevant studies, followed by the definition and
justification of applied taxonomies, as well as descriptions of how the
taxonomies are used to categorize and structure further discussion.

###  3.1 Selection Process

The selection process comprised the definition of concise acceptance criteria,
identification of relevant publication indexes, query definition, two rounds
of article screenings, and final in-depth reading of the remaining candidate
articles. This section presents the acceptance criteria, details the queries
and how they were defined, and presents a full overview of the number of
studies involved in each step of the selection process.

####  3.1.1 Acceptance criteria

Five acceptance criteria have been defined in line with our goals of examining
the existing literature of tangible models considering consumer-side fairness
in recommender systems:

  1. 1.

The study considers recommender systems, see Section 2.2.

  2. 2.

The study considers consumer-side fairness, either explicitly or through a
multi-stakeholder focus.
Note, Group recommendation and Long tail/Cold-start recommender systems are
excluded, see Section 2.4.

  3. 3.

The study is published in a peer-reviewed conference or journal.

  4. 4.

The study proposes a novel model or method.

  5. 5.

The study evaluates the fairness of the proposed model or method.

####  3.1.2 Query Definition and Overview

The keywords were kept general to avoid filtering out potential relevant
research. The search queries were chronologically bound by 2016-01-01 and
2022-10-01, where the lower bound was set based on prior knowledge of the
topic and preliminary querying for validation purposes. The topic started
gaining noticeable traction in 2017, but the early adopters had three
publications before this, (Kamishima et al, 2012, 2013, 2016). The first two
articles do not appear to have inspired other researchers, but since 2016,
there has been a gradual increase in the number of articles each year.

The chronological bound was combined with the keyword combination “recommend*”
and “fairness”, and both keywords had to be matched in the title, the
abstract, or both. “Recommend” was given a wildcard suffix matcher to match
both “recommender” and “recommendation”. A similar wildcard, “fair*”, was used
instead of “fairness” in the DBLP index to compensate for not being able to
match within the abstracts. Observations in known research and research found
through preliminary querying confirmed that all articles that matched “fair”
in the title also matched “fairness” when considering the abstract. The
wildcard was only used in title-only queries since it significantly increased
the number of false positives when matching in both title and abstract.
Fairness is becoming a well-established concept within the ML community, and
most, if not all, research uses the full term at least once before potentially
switching over to the shorthand “fair”.

The full selection process is detailed in a PRISMA flow diagram (Page et al,
2021) in Figure 1.

Figure 1: A PRISMA flow diagram illustrating the full selection process.

###  3.2 Taxonomy

While there have been previous attempts at proposing novel taxonomies for
categorizing fairness approaches in recommender systems based on which
Fairness Interpretation is pursued, we argue that there are alternative
taxonomies that offer additional insight and value. The most recent taxonomy
is proposed by Wang et al (2022), who first proposes splitting between process
and outcome focus, then two alternatives for splitting outcome-focused
fairness on target and concept. One challenge when applying this to consumer-
side fairness research is that many of the named concept-based fairness
categories do not occur that often, and the vast majority of identified
research would be classified as either optimizing and evaluating for Process
Fairness or Consistency Fairness. We also argue that there may be value in
further separating different high-level Fairness Interpretations, e.g.,
Consistency Fairness may consider distance notions that only compare the
distribution of predictions given to different groups, but it can also
consider distance notions that measure differences in how the predictions of
the same groups match the targets.

We propose a new taxonomy centred on which high-level Fairness Interpretation
is considered when optimizing and evaluating models. Besides resulting in a
balanced segmentation of the identified research, the taxonomy separates key
differences in mentality when approaching fairness, some of which
fundamentally conflict with each other. To further structure and analyze the
research, we propose applying two other, more established, concepts which
detail how/when the fairness consideration is incorporated and which type of
recommender model is applied, respectively.

####  3.2.1 Fairness Interpretation Taxonomy

While several fairness definitions from the fields of law and psychology have
been formally defined for machine learning, see Section 2.3, they cannot
trivially be applied for categorizing the studies considered in this survey.
The formal definitions are occasionally implemented as metrics, but since they
mostly consider the model’s outcome, it is challenging to define how they
should be adhered to during optimization. Another challenge is that some of
these definitions are conceptually similar and only differ in minute details.
We instead propose categorizing the Fairness Interpretation on a higher and
more conceptual level, while remaining compatible with the more low-level
formal definitions. For instance, Equality of Opportunity and Equalized Odds
share a high-level objective of balancing utility measures evaluated for
different sensitive groups that consider both the predictions and how they
match the targets. Two identified interpretations have further been assigned
sub-categories for finer distinctions between similar concepts. The full
taxonomy is illustrated in Figure 2, and the different interpretations are
further described in the following sections and illustrated in Figure 3.

Figure 2: The proposed taxonomy based on Fairness Interpretation. Figure 3:
Diagram that illustrates the high-level differences between the three non-
Custom Fairness Interpretations in a scenario where the sensitive groups
$s_{1}$ and $s_{2}$ display different preferences and the base recommender
perform better for $s_{1}$. The preferences and recommendations given to the
groups are illustrated as probability distributions, while model
representations are projected into two-dimensional scatterplots. The
Recommendation Parity interpretation idealizes when the recommendation
distributions overlap, while a Utility-Based interpretation requires that the
respective recommendation distributions match and mismatch the “true”
distributions equally. The Neutral Representation interpretation is optimized
to move from the case where representations of different groups can be
separated into distinct clusters to the case where the clusters overlap or are
indistinguishable.

##### Recommendation Parity

Recommendation Parity methods consider the distribution of ratings, rankings
or preference scores. The Recommendation Parity-based approaches and metrics
are strictly applied for group fairness views and are optimized when the
recommendation distribution given to different users is similar. The strong
focus on recommendation distribution, while completely disregarding
differences in the achieved utility of different sensitive groups, makes
Recommendation Parity a highly contrasting Fairness Interpretation to Utility-
Based fairness and various Custom Fairness Interpretations.

Recommendation Parity for consumer side fairness can be further split based on
at which level the parity is optimized or measured. Some optimize and measure
parity at a global level, while others consider parity in the rating of
individual items or item groups. The former is less constricting, as sensitive
groups may disagree on individual items as long as the disagreements cancel
out globally, i.e., if one group is more fond of an item than another, perfect
global parity is regained if an identical reversed profile exists for another
item. Local-level parity requires different sensitive groups also to
rate/prefer individual items/item groups similarly.

##### Neutral Representation

Adversarial and orthogonality approaches both consider the case where the
model is oblivious to the sensitive attributes of the users fair and achieve
this by making sure the intermediate representations of users do not reflect
any of their sensitive information. A special case of this, achievable through
modelling latent variables independent of the sensitive variables in causal
models, is defined as Counterfactual Fairness by Kusner et al (2017).
Counterfactual Fairness is considered an individual form of fairness, in the
sense that changing the sensitive attributes in individual cases should not
affect the outcome. In the more general case, the indiscriminate and global
removal of sensitive information based on correlations between sensitive
attributes and representations arguably resembles Recommendation Parity more,
as recommender systems using sensitive-neutral representations should
inherently lead to sensitive-neutral recommendations. However, given the
unique perspective of focusing on representations rather than the
recommendations, characteristic optimizations, representation-centric
evaluation, and overall prevalence of approaches, a dedicated interpretation
category for neutral user representations is still deemed warranted.

There are no conceptual sub-categories of this Fairness Interpretation, but
four main strategies for neutralizing representations have been identified:
Adversarial, Orthogonality, Fairness-aware sampling and Probabilistic.
Succinctly, adversarial approaches train classification models to discriminate
sensitive attributes from user representations. These models are trained in
parallel with the main model(s), and their insights are used to inform the
main model how it should be updated to make it harder for the adversarial to
discern sensitive attributes accurately. Proposition 2 from Goodfellow et al
(2014) propose that given a generator model and an adversarial model with
sufficient capacity, the generator can be trained to generate data adhering to
the original data distribution. By replacing the considered task with the task
of distinguishing a binary sensitive attribute given representations, a
similar proposition can be made for adversarial approaches for producing
neutral representations, i.e., given sufficient capacities, neutral
representations are achievable.

Orthogonality approaches utilize the notion of representation space in
considering the representations to be vectors in a high-level semantic space.
They identify sensitive dimensions in said space and apply different methods
to ensure that the representations are orthogonal to these dimensions. Thus,
the representations will ideally not contain any intrinsic sensitive
information themselves.

Fairness-aware sampling and probabilistic modelling have also been used to
reduce the amount of sensitive information in representations of different
flavours. Fairness-aware sampling approaches alter sampling done when training
representations to be more diverse with respect to sensitive attributes.
Probabilistic approaches for producing neutral representations typically
explicitly provide or model sensitive information during training, which
disincentivizes the rest of the model from modelling the same sensitive
information.

##### Utility-Based Fairness

Utility-Based fairness is a comprehensive class focusing on differences in
utility aspects of the recommendations given to different sensitive groups or
different individuals. That is, the distribution of recommendations of
different individuals/groups is free to differ significantly as long as it
does not affect the utility of various entities in a way deemed unfair
relative to the utility of other entities. The one key requirement of the
utility that separates this interpretation from the other interpretations is
that the utility functions considered must be tied to the ground truth targets
in some way. That is, correctly recommending an item will directly affect the
utility value.

Numerous variations of optimization terms and metrics fall under this
interpretation, as the notion of fairness may depend on the utility measure
and the scenario. The observed variations are based on equal recommendation
metric scores, equal utility variance, or the loss of individual utility in
two-sided fairness settings etc.

##### Custom

The final interpretation encompasses measures of adherence to custom fairness
definitions and is a collection of optimizations that do not fit in any other
interpretation category, e.g., parity with respect to derived attributes or
balancing of custom utility measures that are independent of the ground-truth
targets.

####  3.2.2 Fairness Incorporation

The notions of pre-, in- and post-processing methods for injecting additional
specialized considerations in approaches are well established both within the
field of recommender system fairness and machine learning as a whole (Caton
and Haas, 2020; Mehrabi et al, 2021; Deldjoo et al, 2023), and categorize if
the methods take place before, within or after the application of the model
they enhance. To structure the identified research, we propose extending this
taxonomy with an additional level to represent better the observed variety of
approaches applied to incorporate fairness awareness. The second level
contains a single sub-category each for pre- and post-processing approaches,
but we propose four sub-categories to cover the diversity of in-processing
methods. The full overview is illustrated in Figure 4, and each proposed sub-
category has been given a brief description in this section.

Figure 4: Fairness Incorporation categories.

##### Data Augmentation:

The only sub-category of pre-processing methods is Data Augmentation, which
covers all methods that inject fairness consideration by augmenting the
model’s input data.

##### Loss enhancement:

Loss enhancement methods encourage fairness consideration through additional
terms in the loss used for optimizing the model. Positive aspects of loss
enhancement methods are that they can be applied to many model types, are
flexible in definition, and can significantly change predictions through
minimal changes to an approach. However, extra loss terms do not inherently
improve the modelling capacity of a model but may introduce more complex
dynamics that would benefit from more modelling capacity or changes to the
model architecture.

##### Probabilistic:

The probabilistic fairness approaches apply probabilistic concepts to
encourage independence of recommendation and sensitive features, apply soft
constraints, or filter out sensitive information. Unlike the other in-
processing sub-categories, probabilistic fairness approaches are not easily
achieved through a smaller extension to an arbitrary model. This variation of
Fairness Incorporation usually requires that the applied model is
probabilistic in nature itself, at least partially.

##### Algorithmic:

Algorithmic approaches incorporate fairness by changing smaller aspects of an
existing algorithm or through one-time processing, e.g., through selective
sampling or removal of sensitive projections in representation space.

##### Adversarial:

Adversarial approaches apply adversarial models to identify sensitive
information from intermediate representations, to identify how the main model
can be updated to better filter out sensitive information.

##### Re-Ranking:

Re-ranking approaches re-rank the recommendation of one or more base
recommender systems according to new or changed objectives, e.g., introducing
fairness objectives that are optimized along with regular recommendation
utility.

####  3.2.3 Model Types

A third categorization system is used to categorize approaches by which type
of recommender system model architectures they fall under. The model type can
affect how fairness awareness can be incorporated and influence the general
recommendation task. Comparing approaches based on the same model types is
also enhanced by sharing similar implementation details and premises. Several
model groups have been defined based on the prevalence and shared concepts and
can be found listed by an acronym and a description in the following list.

  * •

CF:  Neighbourhood-based Collaborative filtering.

  * •

MF:  Matrix-Factorization.

  * •

NCF:  Neural Collaborative Filtering, taken to mean neural network-based
collaborative filtering methods that more specialized model groups do not
cover.

  * •

Graph:  Various Graph-based models and methods. Graph Neural Networks, Graph
Convolutional Networks, Graph Embeddings etc.

  * •

AE:  (Variational) Auto Encoders.

  * •

Probabilistic:  Various Probabilistic models and methods. Probabilistic Soft
Logic, Latent models, Bayesian Networks etc.

  * •

Classification:  Various Classification methods. Random Forest, Gradient
Boosting, Naive Bayes etc.

  * •

Bandit:  Contextual Bandit.

####  3.2.4 Structuring of Main Discussion

The three different categorizations will all be used when discussing and
comparing the identified approaches. Three sections are reserved for pre-, in-
and post-processing Fairness Incorporation approaches, and their content is
structured by the corresponding Fairness Incorporation sub-categories and both
Fairness Interpretation and model types. The Fairness Interpretation taxonomy
is used in an overview and for a focused comparison of fairness optimization.
In contrast, model types are used to structure a more general technical
discussion to highlight comparable implementational choices.

###  3.3 Full Model Overview

This section presents a preliminary analysis and overview of all identified
research according to model type and Fairness Incorporation method. The motive
is to put the topic into the broader context of general recommender systems
and to provide an overview of all covered research. A full overview is found
in Table LABEL:tab:tax. Note that the same article may fall under multiple
types of Fairness Incorporation and model types, since the proposed approach
may apply multiple types of Fairness Incorporation strategies and be applied
on multiple base models. Also note that while many incorporation methods can
be applied to multiple different model types, especially pre- and post-
processing methods, only observed combinations are covered. The fact that a
method is adaptable for other model types does not guarantee that un-
documented combinations will achieve similar results or improvements.
Furthermore, the current trends of the field are better reflected when keeping
to the combinations that have been actively researched.

Table 3: All covered research categorized by Fairness Incorporation method and recommender system model type. |  Pre-processing | In-processing |  Post-processing
---|---|---|---
|  Data augmentation |  Loss Enhancement |  Probabilistic |  Algorithmic |  Adversarial |  Re-ranking
CF |  Slokom et al (2021) |  Burke et al (2018) |  |  |  |  Patro et al (2020b),
Ashokan and Haas (2021),
Wu et al (2021c)
MF |  Rastegarpanah et al (2019),
Fang et al (2022),
Slokom et al (2021) |  Kamishima et al (2012),
Kamishima et al (2013),
Kamishima and Akaho (2017),
Yao and Huang (2017),
Kamishima et al (2018),
Zheng et al (2018),
Wan et al (2020),
Yao and Huang (2021) |  |  |  Resheff et al (2019),
Li et al (2021b),
Wu et al (2021b) |  Edizel et al (2020),
Patro et al (2020a),
Patro et al (2020b),
Wu et al (2021c),
Ashokan and Haas (2021),
Biswas et al (2021),
Do et al (2021),
Wu et al (2022a)
NCF |  |  Bobadilla et al (2021),
Islam et al (2021),
Wu et al (2021a),
Li et al (2021a) |  |  Islam et al (2019),
Islam et al (2021),
Li et al (2022b) |  Li et al (2021b),
Wu et al (2021a)
Wu et al (2022b),
Wei and He (2022),
Rus et al (2022) |  Wu et al (2022a)
Graph |  |  Liu et al (2022c),
Liu et al (2022a) |  Buyl and Bie (2020),
Li et al (2022a) |  Rahman et al (2019),
Xu et al (2021),
Li et al (2022b) |  Bose and Hamilton (2019),
Wu et al (2021b),
Xu et al (2021),
Liu et al (2022c),
Liu et al (2022b),
Liu et al (2022a) |
Probabilistic |  |  |  Kamishima et al (2016),
Farnadi et al (2018),
Buyl and Bie (2020),
Dickens et al (2020),
Frisch et al (2021),
Li et al (2022a) |  |  |  Dickens et al (2020)
AE |  |  Li et al (2021a),
Borges and Stefanidis (2022) |  |  |  Borges and Stefanidis (2022) |
Classification |  |  |  |  |  |  Paraschakis and Nilsson (2020)
Bandit |  |  Huang et al (2021) |  |  |  |

####  3.3.1 Model Analysis

Some clear trends can be observed in the full table. The field has experienced
rapid growth, with most research taking place in the most recent years. Pure
loss enhancement approaches saw a lot of attention among the early adopters,
especially when used together with matrix factorization models but are
currently rarely used as the sole Fairness Incorporation method. Re-ranking
methods saw a similar burst of attention in 2020 and 2021. Still, they did not
dominate the field, unlike early loss enhancement approaches, as multiple
other directions were researched simultaneously. Adversarial approaches were
slow to appear but have since become popular while seemingly being used with a
more varied selection of base recommender system types. Bayesian and
algorithmic approaches are the smallest in-processing groups but are
characterized by being pretty evenly distributed across time and being applied
with specific types of recommender systems. There also appears to be a recent
trend of applying multiple Fairness Incorporation strategies instead of
relying solely on a single strategy.

##  4 Pre-Processing Methods

While numerous studies consider the effect of data augmentation, we only found
three papers that pass all acceptance criteria. In particular, several
candidates were rejected for not proposing formalized approaches or not
presenting an evaluation of the achieved fairness. Pre-processing methods
comprise the smallest Fairness Incorporation main category.

###  4.1 Fairness Optimization

Table 4: Overview of the identified pre-processing approaches structured by the Fairness Interpretation and Fairness Incorporation of their optimization. Approaches that consider multiple Fairness Interpretations are listed in multiple rows. |  |  Data Augmentation
---|---|---
Recommendation Parity |  Global |  Fang et al (2022)
|  Local |
Neutral
Representation |  |
Utility-Based |  Group |  Rastegarpanah et al (2019)
Fang et al (2022)
|  Individual |  Rastegarpanah et al (2019)
Custom |  |  Slokom et al (2021)

####  4.1.1 Utility-Based Fairness

Rastegarpanah et al (2019); Fang et al (2022) propose exploiting collaborative
filtering dynamics by training new synthetic users that will influence the
recommendation of the real users. When training synthetic user, Rastegarpanah
et al (2019) enhances the loss by adding terms for penalizing both the group-
level and the individual-level variance of mean squared errors. In contrast,
Fang et al (2022) utilize similar loss terms based on the utility metrics
proposed by Yao and Huang (2017), see Section 7.3.1, and also global
Recommendation Parity.

####  4.1.2 Custom

The fairness optimization proposed by Slokom et al (2021) shares similarities
with in-processing approaches optimizing for Neutral Representations but
alters the input data to remove correlation between the user profiles and the
sensitive attributes of the users, instead of altering the intermediate user
representations. The approach achieves this by adding items that are
indicative of the other sensitive groups, identified using auxiliary models,
to the user profiles, and they also explore removing items at random or based
on how indicative they are of the actual sensitive attributes of the user.

###  4.2 Architecture and Method

The three selected papers all propose pre-processing methods that can be
applied to a wide variety of model types, but all have used matrix
factorization as one of their base recommender models. Rastegarpanah et al
(2019) propose a method for training supplementary data that can influence
polarization and improve individual and group fairness. The key insight is
that introducing additional users will affect the recommendation of the
original users. This insight is exploited by adding a few synthetic users with
accompanying data and allowing gradients from loss terms designed to influence
the polarization and fairness to flow back to these. Further, they propose two
computationally cheap heuristics. The fairness optimization idealizes equal
utility of individual users and groups explicitly. Fang et al (2022) apply the
same base approach but focus on optimizing multiple fairness objectives more
efficiently and smoothly by projecting the gradients of different objectives
onto each other if they conflict. The fairness objectives fall under both
Utility-Based fairness and Recommendation Parity.

Slokom et al (2021) modify the data of existing users through an extension of
the approach proposed by Weinsberg et al (2012) instead of training new ones.
An auxiliary logistic regression model is trained to tell how indicative items
are of the gender of the users that like them. This information is used to
select items to be added or removed from user data to make the data less
indicative of gender. The addition process specifically intersects lists of
indicative items with recommendations from a user-based collaborative
filtering model to motivate the addition of relevant items.

##  5 In-Processing Methods

In-processing methods are the most represented among the main categories, and
their dominance has been constant since the birth of the field. They are
characterized by being the most specialized approaches, as the base models
themselves are adapted and changed.

###  5.1 Fairness Optimization

Table 5: Overview of the identified in-processing approaches structured by the Fairness Interpretation and Fairness Incorporation of their optimization. Approaches that consider multiple Fairness Interpretations and Fairness Incorporation methods are listed in multiple rows and columns. |  |  Loss Enhancement |  Probabilistic |  Algorithmic |  Adversarial
---|---|---|---|---|---
Recommendation Parity |  Global |  Kamishima et al (2012)
Kamishima et al (2013)
Kamishima and Akaho (2017)
Kamishima et al (2018) |  Kamishima et al (2016)
Dickens et al (2020) |  |
|  Local |  Kamishima et al (2013)
Islam et al (2021) |  Farnadi et al (2018) |  |
Neutral Representation |  |  Wu et al (2021a)
Liu et al (2022c)
Liu et al (2022a) |  Buyl and Bie (2020)
Frisch et al (2021)
Li et al (2022a) |  Rahman et al (2019)
Islam et al (2019)
Islam et al (2021)
Xu et al (2021)
Li et al (2022b) |  Resheff et al (2019)
Wu et al (2021a)
Xu et al (2021)
Borges and Stefanidis (2022)
Bose and Hamilton (2019)
Li et al (2021b)
Wu et al (2021b)
Liu et al (2022c)
Wu et al (2022b)
Liu et al (2022b)
Liu et al (2022a)
Wei and He (2022)
Rus et al (2022)
Utility-Based |  Group |  Yao and Huang (2017)
Zheng et al (2018)
Wan et al (2020)
Huang et al (2021)
Yao and Huang (2021)
Liu et al (2022c)
Borges and Stefanidis (2022) |  Dickens et al (2020) |  Li et al (2021a) |
|  Individual |  |  |  |
Custom |  |  Burke et al (2018)
Wan et al (2020)
Bobadilla et al (2021) |  |  |

####  5.1.1 Recommendation Parity

Optimization of Recommendation Parity fairness, i.e., the statistical parity
of recommendations given to different sensitive groups, is mainly found among
the in-processing methods and was popular during the field’s early years.

##### Global Recommendation Parity:

Kamishima et al (2013); Kamishima and Akaho (2017) propose adding loss terms
for matching mean rating and preference of different sensitive groups, while
Dickens et al (2020) devise a probabilistic soft logic rule of similar design
for the same goal.

More comprehensive approaches for matching global recommendation distributions
beyond the first momentum are proposed by Kamishima et al (2012, 2016, 2018).
Kamishima et al (2012, 2018) introduce different loss terms for minimizing the
mutual information of the ratings and the sensitive groups in matrix
factorization. In a slightly different approach, Kamishima et al (2016) apply
a latent factor model where the rating variable is considered independent of
the sensitive group variable and optimizes their model using the Expectation
Maximization algorithm.

##### Local Recommendation Parity:

In the case of local Recommendation Parity, all relevant research we have
found only considers the first moment when matching the recommendations of
different sensitive groups. Kamishima et al (2013) propose adding a loss term
that penalizes the squared difference of item ratings between different
sensitive groups as an alternative to the already mentioned global version.
Similarly, Islam et al (2021) apply the same idea but opt for an absolute
difference instead of a squared difference. The probabilistic soft logic
approach proposed in Farnadi et al (2018) defines rules for encouraging both
item-group and item-level parity.

####  5.1.2 Neutral Representation

The objective of Neutral Representation fairness cannot be achieved without
altering the model, thus, it is only pursued by in-processing approaches.
Optimization of this Fairness Interpretation can be achieved by applying
different strategies for filtering out intrinsic sensitive information in
representations within the model. The following paragraphs are structured by
the technique applied to achieve neutral representations, see also Fig 4.

##### Adversarial:

The approaches proposed by Resheff et al (2019); Wu et al (2021a); Xu et al
(2021); Borges and Stefanidis (2022); Rus et al (2022) all apply adversarial
models directly on model representations. Resheff et al (2019) pass the latent
user factors of their matrix factorization approach to their adversarial,
while Wu et al (2021a) do the same with one of the multiple user
representations they train in a composite NCF model. Xu et al (2021) feed
their adversarial model a linear combination of the user representation in a
base recommender model and a representation they base on an auxiliary
knowledge graph for modelling sensitive user attributes. Rus et al (2022)
propose a neural classification model and applies an adversarial model on a
hidden layer in the said model. Finally, Borges and Stefanidis (2022) apply an
adversarial model to discriminate the latent representation in their
variational autoencoder-based model.

A slightly more intricate scheme is proposed by Wei and He (2022), who
concatenate the observed ratings to the representations that are fed to the
adversarial model, which they argue will improve the neutrality of the
representation and also make the representations independent with respect to
the sensitive attribute conditioned on the observed ratings. They further add
a second adversarial model, which is fed predicted ratings along with
corresponding observed values and item embeddings.

Bose and Hamilton (2019); Li et al (2021b) argue for letting users dynamically
decide which sensitive attributes they are comfortable with the model using.
To support this, both propose training optional filters for filtering out
different types or combinations of sensitive information from user
representations in graph- and matrix-factorization models. The filters are
trained using adversarial models. A similar approach is proposed by Wu et al
(2022b), who train adaptors (Houlsby et al, 2019) within the transformers
(Vaswani et al, 2017) that make out their model. The adaptors dynamically
filter out different combinations of sensitive attributes based on user- and
task-based settings in a sequential recommendation setting.

Wu et al (2021b); Liu et al (2022a, b, c) all consider graph neural network
methods and the construction of higher-order graph representations by
accumulating neighbouring representations in the recommendation graph. The
approaches apply adversarial models to discourage the encoding of sensitive
attributes in the user- and item-level representations, which also mitigate
the accumulation of sensitive information in the higher-order neighbourhood
representations. Liu et al (2022c) further supplements the adversarial
discrimination loss with a loss term on the covariance of the predicted
attribute and the actual sensitive attribute. Liu et al (2022a) instead
designs and utilizes self-supervising loss terms to enhance the
representations and mitigate imbalance issues caused by imbalanced sensitive
attributes.

##### Orthogonality:

Orthogonality-based approaches apply additional loss terms or explicit removal
of sensitive projections to make representations orthogonal to explicit or
implicit sensitive dimensions in the representation space. Wu et al (2021a)
model two separate user representations: one for inferring sensitive
information and one for providing neutral representations. They devise a loss
term that encourages the two representations to be orthogonal and further
encourages the neutrality of the second representation through an adversarial
approach.

A more explicit approach is pursued by Islam et al (2019, 2021), where a post
hoc step infers sensitive dimensions in the representation space by taking the
difference of the mean representation of each sensitive group. The projections
of the sensitive dimension onto each representation are then explicitly
subtracted. In the case of Islam et al (2021), the orthogonality processing
supplements the Recommendation Parity loss term (see Section 5.1.1).

##### Sampling Based Representation Training:

Rahman et al (2019); Li et al (2022b) both adjust the sampling strategy used
when training representations. Rahman et al (2019) proposes to balance the
sampling of the next user according to sensitive groups when training graph
representations using random walks. In contrast, Li et al (2022b) adjust the
probability of sampling the triplets needed for training knowledge graph
representations in a manner that balances out the correlation of sensitive
groups and items across all users.

##### Probabilistic Approaches:

The models by Buyl and Bie (2020); Li et al (2022a) are fitted using a prior
that is informed of sensitive attributes to allow the rest of the model to
focus on other aspects. When the model is used, the sensitive prior is
replaced by one oblivious to the sensitive attributes. The intention is to
produce fair recommendations along with neutral representations.

Frisch et al (2021) explicitly model a variable for representing the
contribution of the sensitive attributes instead of using a sensitive prior.
Ideally, this sensitive variable can soak up all sensitive information,
leaving the rest of the model neutral. When recommending, the model drops the
parts of the model that are dependent on the sensitive attribute.

####  5.1.3 Utility-Based Fairness

Utility-Based fairness optimization attempts to balance utility measures that
involve ground truth consideration on a group or individual level. While only
group-level optimizations are found among the in-processing methods, there is
still significant variation in the considered approaches.

Yao and Huang (2017) proposes four Utility-Based fairness metrics for
recommender systems, then adapt and applies each metric as loss terms in a
matrix factorization approach. One of the metrics is similarly adapted by
Dickens et al (2020) as a probabilistic soft logic rule.

Numerous variations of straight-forward loss terms based on Group Utility-
Based Fairness Interpretations are proposed for different models: the
contextual bandit approach proposed by Huang et al (2021) penalizes
differences in cumulative mean rewards of different sensitive groups. Liu et
al (2022c) and Borges and Stefanidis (2022) both supplement adversarial
approaches with Utility-Based fairness loss enhancement. Liu et al (2022c)
penalize the absolute differences in pairwise recommendation loss of different
sensitive groups, while Borges and Stefanidis (2022) penalize differences in
reconstruction loss of a protected group and that of the average user in their
variational autoencoder model. Finally, Yao and Huang (2021) train
personalized regularization weights based on the loss of a specific sensitive
group to force the matrix factorization model to focus more on their achieved
utility.

Wan et al (2020) considers a unique recommender system setting where users and
items are segmented into market segments based on sensitive groups and item
groups and argue that the utility within the market segments should be
similar. The proposed model applies loss terms that penalize error variation
between user groups, item groups, and market segments. The authors also
explore a market segment-level parity alternative by penalizing the variances
of predicted ratings instead of errors.

Li et al (2021a) propose a less direct way of encouraging the model to value
the utility of non-mainstream user groups more by adding decoder components to
their representations and corresponding loss terms for reconstructing the
inputs. The intention is to provide the model with a stronger incentive for
properly encoding all users and items, which in turn may mitigate issues with
favouring the utility of mainstream user groups at the expense of everyone
else. A similar goal is pursued by Liu et al (2022a), who devise a set of
auxiliary goals for encouraging their model to produce richer representations
of all users.

For the reciprocal setting, Zheng et al (2018) proposes to consider both the
utility of the user that receives the recommendation and the utility of the
recommended users themselves. On a global level, this scheme balances the
utility of two user groups based on the user’s role in individual
recommendations, i.e., reference users and users being recommended to
reference users.

####  5.1.4 Custom

Bobadilla et al (2021) utilize empiric trends in the input data to design a
set of indexes that represent users’ and items’ intrinsic sensitive value.
They further design a loss term to penalize recommending items to users if the
index values differ significantly. Loss enhancement is also applied in the
neighbourhood-based collaborative filtering model proposed by Burke et al
(2018) to balance the contribution of peers of different sensitive groups when
recommending. Specifically, the added loss term penalizes the absolute
difference of the model-specific user-to-user weights of different sensitive
groups.

###  5.2 Architecture and Method

####  5.2.1 Loss enhancement

##### Matrix Factorization

The early works of Kamishima et al; Kamishima et al are the earliest
identified research that satisfies all acceptance criteria in this survey. The
four publications (Kamishima et al, 2012, 2013, 2018; Kamishima and Akaho,
2017) all propose matrix factorization models where the fairness aspects are
modelled through different, but related loss terms. They all share the overall
goal and fairness objective of ensuring statistical parity of recommendations.
Additionally, all train different sets of parameters for the different
sensitive groups they consider. In the first iteration, Kamishima et al (2012)
propose a loss term that is an approximation of the mutual information of the
rating and the sensitive attributes. Next, Kamishima et al (2013) introduces
an efficiency improvement with alternative loss terms that penalize differing
ratings per sensitive group averaged over all items or individually. The paper
by Kamishima and Akaho (2017) considers similar loss terms, but through a
implicit-feedback recommender system using ranking-based evaluation. It is
noted that the approach has little effect on the ranking order of each user.
Finally, Kamishima et al (2018) returns to rating-based recommender systems,
introducing two new methods matching the first and second moment of the
distributions for ensuring statistical parity. Both methods approximate rating
distributions given the sensitive attribute with normal distributions, and
then penalize Bhattacharyya distance (Bhattacharyya, 1943) and mutual
information respectively.

Another early contribution was by Yao and Huang (2017), who argue for fairness
definitions based on matching utility rather than Recommendation Parity. They
propose four new Utility-Based unfairness metrics that measure imbalances in
how well the system recommends for different sensitive groups. Further, they
devise loss terms based on these metrics and an additional parity-based metric
to compare how well models trained with the different loss terms fare when
evaluated using all metrics.

Zheng et al (2018) is concerned with recommending matches after speed-dating,
which is a reciprocal recommendation setting in the sense that consumers are
recommended to other consumers. The model predicts user impression of speed-
dates with different partners and considers a Custom utility metric based on
the similarity of user’s expectation of a partner and their impression of the
speed-date partner. The utility metric is also used in the added loss term,
which is designed to maximize the utility of both users in each potential
match. The motivation is to balance the utility achieved by users being
recommended for and the utility achieved by the users said users are
recommended. Considering the utility of both involved users may also improve
the overall success of this specific application, as mutual interest is ideal
in a matchmaking scenario.

The approach proposed by Wan et al (2020) is designed to address retail
marketing bias by better balancing the achieved utility in different market
segments. In particular, they define market segments based on sensitive user
groups and attributes of models used in marketing different items, e.g., one
segment may make out male users and items only marketed using female models.
The proposed approach attempt to achieve similar utility within each distinct
market segment by penalizing error variance between the different segments and
other groupings. An alternative configuration is also considered where the
model instead penalizes predicted rating variance, resulting in a
Recommendation Parity Fairness Interpretation.

The last identified loss enhancement-based matrix factorization approach was
proposed by Yao and Huang (2021). The key idea of the model is to improve the
utility of disadvantaged users through personalized regularization. This is
achieved through a multi-step process that alternates between training for the
general recommendation task while keeping the personalized regularization
weights static and updating the same parameters based on the recommendation
loss of the disadvantages.

##### Neighbourhood-based Collaborative Filtering

Burke et al (2018) propose enhancing the loss of a user-based collaborative
filtering approach to encourage users’ neighborhood of peers to be better
balanced with respect the considered sensitive attributes. To this end, they
devise a loss term that penalizes if the coefficients used for weighting
influence of peers are skewed towards a specific group, i.e., the sum of male
peer coefficients is greater than that of female peers.

##### Neural Collaborative Filtering

Bobadilla et al (2021) are unorthodox in terms of fairness definition and
approach. They give each item a value based on the distribution of, e.g., the
gender of users who like it, thus representing how gendered the item is. The
items are then used reversely to measure how gendered each user is based on
the items they like. The authors go on to penalize recommending items with a
gendered value far from the user’s.

Li et al (2021a) aims to improve the utility of collaborative filtering models
for users that are not mainstream. Their approach involves a factorization
step that involves user and item representations, where the representations
double up as the latent representations in two autoencoders. The autoencoders
are added to encourage the model to properly encode all input information in
the latent representations, and not neglect information only relevant to a
subset of the users.

##### Bandit

The only identified bandit approach was proposed by Huang et al (2021), and is
a contextual bandit method that penalizes differences in cumulative mean
rewards of different sensitive groups. The authors construct a synthetic
dataset for video recommendations and define a reward function that, for
instance, rewards cases where the gender of the user and the video speaker is
the same.

####  5.2.2 Probabilistic

##### Graph

Buyl and Bie (2020) consider link prediction in social graphs and applies a
probabilistic model for training graph representations based on the work by
Kang et al (2019). They encode prior knowledge of the relations in the network
using a prior term, which frees up the representations from encoding the same
knowledge. Buyl and Bie (2020) leverage this by designing priors that contain
sensitive information to be used during training but replaced in the final
recommendations. Li et al (2022a) further adapt the approach for peer
recommendation in online learning and introduce changes to the negative
sampling used during training.

##### Probabilistic Model

Farnadi et al (2018) and Dickens et al (2020) both apply models based on
Probabilistic Soft-Logic (PSL) (Bach et al, 2017) for fairness-aware
recommendation. PSL allows probabilistic models using human-interpretable
first-order logic. Both models apply a base set of logical rules for the
general recommendation task, e.g.,

$\displaystyle\text{SIMILAR\\_USER}(u_{1},u_{2})\land\text{RATING}(u_{1},i)\implies\text{RATING}(u_{2},i),$
$\displaystyle\text{SIMILAR\\_ITEM}(i_{1},i_{2})\land\text{RATING}(u,i_{1})\implies\text{RATING}(u,i_{2}).$

Farnadi et al (2018) extend the model with fairness rules based on parity,
e.g., one sensitive group’s rating of an item implies the rating of a
different sensitive group and vice versa. Dickens et al (2020) consider
courser parity-based rules and add others for encouraging equal utility for
the different sensitive groups. Further, they allow modellers to adjust the
importance of different fairness terms. They also discuss using the model
together with an arbitrary black-box model to inject fairness and
interpretability, which can be thought of as a form of re-ranking.

In the work by Kamishima et al (2016), two different graphical models are
proposed for modelling ratings independent of a sensitive group membership.
The models are realized as latent class models and optimized through the
Expectation-Maximization algorithm.

Frisch et al (2021) propose using a latent block model for clustering users
and items, then model a new rating-mean based on the associated cluster mean,
individual variables for the item- and user-specific influences, and finally
an item-specific variable that is controlled by the user’s sensitive
attribute. This final variable models the sensitive information, and is only
used during training, similar to how informed priors are used in Buyl and Bie
(2020). The model is optimized using variational inference.

####  5.2.3 Algorithmic

##### Neural Collaborative Filtering

Islam et al (2019) explicitly subtract sensitive projections in user
representations in a neural collaborative filtering model. They consider both
scenarios where there is a single or multiple binary sensitive attribute(s),
e.g., male/female and young/senior. Some of the same authors (Islam et al,
2021) propose a more intricate approach where they utilize transfer learning
to pre-train user representations and neural network weights in a non-
sensitive recommendation setting. The user representations are then processed
similarly as by Islam et al (2019) to be used in a sensitive recommendation
setting. The non-sensitive settings considered are film recommendation and
social media action recommendation, while the sensitive settings are
occupation and college major recommendation, respectively. A parity-based loss
term is applied in addition to the user representation processing to
incorporate fairness in sensitive settings.

Li et al (2022b) propose a fairness-aware sequential recommender system in
which an integral part is to train item representations for representing the
contextual information of the items and their relations. The authors use
fairness-aware sampling when training said representations. Specifically, the
sampling probability is set to adjust for any empirical skewness in how an
item is preferred by different sensitive groups.

##### Graph

The approach by Rahman et al (2019) is designed to be used in reciprocal
settings and tested on recommending peers in social networks while considering
sensitive groups based on gender and race. The base representation algorithm
performs random walks over the graph by sampling the next user among the
current user’s peers, i.e., the users the current user has a relation to in
the observed data. Their fairness view is introduced by first sampling the
peer’s sensitive attribute uniformly, then sampling as usual from the
qualified peers only.

Xu et al (2021) work with knowledge graph-based recommender systems. They
propose training user representations of an auxiliary graph for representing
sensitive attributes and their hidden relationships through a multi-layered
neural network. This user representation is combined with that of the original
recommender system in a linear transformation and then factorized with the
item representation from the original recommender system. Additionally, an
adversarial network is trained to classify sensitive attributes from the
compound user representations and used to filter out said information. The
purpose of the auxiliary graph representation is stated to be to improve the
modelling of multiple sensitive attributes and their interactions.

####  5.2.4 Adversarial

##### Matrix Factorization

Resheff et al (2019) apply an adversarial gradient-based model to remove
information like gender and age in the latent user factors. The authors list
both privacy and fairness aspects as motivations for adversarial filtering.

Li et al (2021b) adopt the approach proposed by Bose and Hamilton (2019) using
multiple different recommender system specific models, as opposed to the more
general setting of link-prediction considered by Bose and Hamilton (2019). The
approach is applied using four different models, covering matrix factorization
and neural collaborative filtering. They further extend the approach by
proposing a secondary option for training single filters for combinations of
sensitive attributes, which is compared to the main approach of training one
filter for each attribute and taking the mean of filtered representations to
apply combinations.

##### Graph

Bose and Hamilton (2019) proposes to filter combinations of sensitive
attributes from graph representations dynamically and considers both link-
prediction and recommender system applications using different setups. They
train one filter per sensitive attribute and combine filters by aggregating
the representations processed by the filters. Each sensitive attribute is
further assigned an adversarial for removing the traces of said sensitive
attribute. A binary mask is sampled during training to simulate different
users who want to restrict the use of different combinations of sensitive
attributes. This mask is used in practice to activate the respective filters.

Wu et al (2021b) assume a graph-based perspective and that pre-trained user
and item representations are provided. They suggest training filter functions
for filtering out sensitive information from both representations and using
these to build higher-order neighbourhood representations iteratively. For
instance, the first-order neighbourhood representation of a user is based on
the filtered representations of the items the user has liked or interacted
with, the second-order neighbourhood contains the first-order neighbourhood
representation of the same items, and so on. A multi-layered neural network is
used to simultaneously process the first- and second-order neighbourhood
representations into the final network level representation, with the
motivation to capture higher-order sensitive information and how the different
levels relate. Adversarial models are applied to both the filtered initial
user representations and the final network-level user representations.

Liu et al (2022a, b, c) also apply neighbourhood representations, along with
adversarial models for removing sensitive information in the base
representations. However, they differ from Wu et al (2021b) as they consider
end-to-end systems where the base representations are trained as part of the
same model, and in using the highest-order representations explicitly as the
final representations. The three papers themselves differ in how they
construct higher-order neighbourhood representations. Liu et al (2022a, c)
reduce the contribution of higher-order representations by dividing with a
function that increases linearly in the order. Liu et al (2022b) construct
higher-order representations by passing the previous-order representations
through a neural network and also explicitly considers the representations of
neighbours that are increasingly further removed in the graph. The approaches
further differ in their application of additional fairness optimization. Liu
et al (2022c) propose two new loss terms: one for penalizing the covariance of
the actual sensitive attribute and the one outputted by the adversarial model,
and another for penalizing differences in pairwise losses of different
sensitive groups. The former further enhances the neutrality of the
representations, while the latter has an equality of utility motivation. .Liu
et al (2022a) proposes to enhance the base representations by designing and
applying a set of loss terms that encourage the representation of more complex
information to mitigate the poor representation of underrepresented sensitive
groups in the dataset.

##### Neural Collaborative Filtering

A neural collaborative filtering model for fairness-aware news recommendation
is proposed by Wu et al (2021a). The key idea is to contain all sensitive
information in a part that can be disregarded when the model is applied,
similar to the priors in Buyl and Bie (2020). Two separate user
representations are trained: one is used for classifying the sensitive
attribute and has the intention of aggregating sensitive information, while
the other is designed for housing everything else and is coupled with an
adversarial model to remove sensitive information. The sum of both user
representations is used for recommendation during training while encouraging
that the representations are orthogonal through adding a loss term. Only the
neutral representation is used once the model is finished training.

Rus et al (2022) propose to improve fairness in a job recommender system by
filtering out gender information in representations of user resumes. To this
end, they first train new word embeddings on resumes and job application texts
within a proprietary dataset. The trained word embeddings are then used to
encode the resume texts, and the encoded texts serve as inputs to their
proposed neural recommender model. An adversarial model is applied to filter
out gender information at a specific layer in the multi-layered neural network
model. The authors also explore a simple alternative where they instead
replace gendered words with neutral words before training the word embeddings.
However, the adversarial approach is shown to outperform this alternative.

Wu et al (2022b) follow Bose and Hamilton (2019); Li et al (2021b) in letting
the users decide which sensitive attributes can be considered when generating
recommendations. However, while the preceding research train multiple filters
for different sensitive attributes that are dynamically plugged into the
recommender system pipeline when activated, the filtering components in Wu et
al (2022b) are static parts of the model that dynamically change behaviour
based on personalized prompts concatenated with the input. The filtering
components are based on the adaptor proposed by Houlsby et al (2019) and
trained along with different discriminators while keeping the remaining model
parameters frozen.

The framework proposed by Wei and He (2022) considers multiple Fairness
Interpretations simultaneously. The framework consists of two main loops: an
inner loop in which users are initialized with the latest parameters suggested
by a meta-model and then optimized for different tasks, and an outer loop
where the results of the inner loop are used to update the parameters of the
meta-model to produce better user initializations in the next cycle. The
framework applies two different adversarial models, which both attempt to
detect sensitive attributes: the first one is fed user representations based
on trained context representations and the users’ observed ratings, while the
second considers the predicted ratings, the corresponding observed ratings,
and item representations.

##### Variational Autoencoder

Borges and Stefanidis (2022) use a variational autoencoder (VAE) as their main
model. The VAE is considered a collaborative recommender, where the decoded
latent representation is interpreted as an encoding from which recommendations
are extracted. The VAE is extended with an adversarial model for training the
model to produce neutral latent representations and a loss term for
encouraging the model to be equally good at reconstructing the inputs of a
specific protected sensitive group as at reconstructing the inputs of all
users on average.

##  6 Post-Processing Methods

Post-processing methods share one of the main benefits of pre-processing
methods in being flexible with respect to which recommender system model is
used. Additionally, post-processing methods do not affect the raw data but are
arguably the least flexible approaches when it comes to modelling since they
are constrained by the provided recommendation and the data used to train the
model. Post-processing methods are not as popular as in-processing methods but
have received more attention than pre-processing methods.

###  6.1 Fairness Optimization

Table 6: Overview of the identified post-processing approaches structured by the Fairness Interpretation and Fairness Incorporation of their optimization. Approaches that consider multiple Fairness Interpretations are listed in multiple rows. |  |  Re-ranking
---|---|---
Recommendation Parity |  Global |  Dickens et al (2020)
Ashokan and Haas (2021)
|  Local |
Neutral
Representation |  |
Utility-Based |  Group |  Ashokan and Haas (2021)
Wu et al (2022a)
|  Individual |  Wu et al (2021c)
Custom |  |  Edizel et al (2020)
Paraschakis and Nilsson (2020)
Patro et al (2020a)
Patro et al (2020b)
Biswas et al (2021)
Do et al (2021)

####  6.1.1 Recommendation Parity

Both the post-processing techniques for Recommendation Parity included in the
survey use the global perspective. Ashokan and Haas (2021) propose using
results from the training data to align better the rating distribution of the
two sensitive groups in a binary setting. To this end, they add the mean
rating difference of the two sensitive groups during training to the predicted
ratings of one of the groups when using the model for a new recommendation.

The approach in Dickens et al (2020) discussed in Section 5.1.1 is also
applicable as a re-ranker of a base recommender model. Thus, their proposed
probabilistic soft logic rule comprises a second identified strategy for
optimizing Global Recommendation Parity in post-processing methods.

####  6.1.2 Utility-Based Fairness

##### Group:

The re-rating approach proposed by Ashokan and Haas (2021) considers a scheme
where the per-item average rating error for each sensitive group, as observed
in the training data, is added to the individual ratings of the users. This
method is analogous to the previously covered parity scheme proposed in the
same research.

The only identified approach that optimizes group Utility-Based fairness in a
two-sided fairness approach is proposed by Wu et al (2022a). Through applying
the Frank-Wolfe algorithm (Frank and Wolfe, 1956), the authors optimize for
consumer-side fairness by minimizing the variance of a differentiable
definition of NDCG, along with the general recommendation and provider-side
fairness objectives.

##### Individual:

A multi-stakeholder approach is proposed by Wu et al (2021c), in which the
consumer-side fairness objective is to fairly distribute the loss of utility
incurred by the producer-side exposure considerations among the users. They
devise a two-step approach, where the first step attempts to identify and fix
highly preferred items that still have to reach their maximum exposure in the
recommendation lists of the users. Each user is assigned one item at a time in
a manner to even out the benefit of choosing first. The second step fills in
the free recommendation slots with the items that still require exposure per
the provider-side objective.

####  6.1.3 Custom

Patro et al (2020a, b); Biswas et al (2021) all consider multi-stakeholder
settings where the consumer-side objective is to distribute the loss of
utility among users fairly. However, unlike Wu et al (2021c), they propose
applying a utility definition that is not tied to the ground truth. Their
shared utility measure is purely based on the preference values outputted by
the original recommender system and produces values indicating how far from
optimal the new recommendations are deemed. Patro et al (2020a) and Biswas et
al (2021) both propose similar two-step approaches as that of Wu et al (2021c)
but opt for guaranteeing the producer-side objective in the first step by
allocating items in need of exposure in turn to users while attempting to
prioritize items preferred by the user. The second step fills the remaining
slots with the users’ most preferred items. Finally, multi-sided fairness in a
dynamic setting is explored by Patro et al (2020b) who attempts to retain both
provider- and consumer-side fairness when facing different incremental changes
to the recommendation, e.g., a gradual transition to a new base recommender
model. Individual fairness is preserved by introducing lower-bound user
utility constraints in the proposed integer linear programming model.

A similar setting is considered by Do et al (2021) whose approach also
optimizes for two-sided fairness and applies custom user utility tied to the
base recommender’s outputted preference scores system. The approach positions
itself to maximize the custom utility of worse-off users and items
simultaneously in both regular and reciprocal recommendation settings.

Edizel et al (2020) focus on providing users recommendations that are
uncorrelated with their sensitive attributes. The goal shares many parallels
with in-processing approaches that optimize for intermediate representations
that are uncorrelated with the sensitive attributes but operate on sets of
recommendations due to the post-processing nature. The key idea is to allow
users to inherit the recommendations of similar or arbitrary users belonging
to different sensitive groups, thus muddying the correlation between the
sensitive attributes and both recommendation lists and individual
recommendations.

Another re-ranking approach is by Paraschakis and Nilsson (2020), which
considers an individual fairness definition based on calibration by user
preferences. Specifically, they consider a matchmaking setting where users
specify how important it is for them to date within their race or religion.
The problem is optimized through dynamic programming.

###  6.2 Architecture and Method

####  6.2.1 Neighbourhood-Based Collaborative Filtering

The approach proposed by Ashokan and Haas (2021) is technically a re-rating
approach since they consider rating-prediction-based recommender systems but
share many similarities with re-ranking approaches. The key idea is to attempt
correct predictions of members of different sensitive groups by adding the
average prediction errors for each item and sensitive group, as observed in
the training set, to new predictions. A second parity-based option instead
adds the average difference of the rating predictions given to different
sensitive groups for each item.

####  6.2.2 Matrix Factorization

Edizel et al (2020) focus on ensuring the generated top-$k$ recommendations
are uncorrelated with sensitive groups by making users inherit the
recommendations of other users belonging to a different sensitive group. While
parts of the approach are enhanced when the same top-$k$ recommendations are
recommended to multiple users by the base recommender system, the approach
also works when all top-$k$ recommendations are unique, which is not unlikely
for a large $k$ and a large item catalogue. Two different schemes for
recommendation inheritance are evaluated: random and based on similarity. The
former is shown to be more effective at reducing how indicative the
recommended set is of the user’s sensitive group but also reduces the utility
quicker.

The works produced by Patro et al (2020a, b); Biswas et al (2021) have an
overlapping set of authors, and all consider the same two-sided recommendation
setting. In Patro et al (2020a), the primary goal is to satisfy minimum
requirements for provider-side exposure, subject to a secondary goal of
distributing the loss of utility among the users fairly. They propose a two-
step approach where first items are distributed among the user by allocating
one item per user in turn to satisfy the items’ minimum exposure criteria. The
users are given the best remaining item according to said user’s predicted
preferences. Secondly, the remaining recommendation list of each user is
filled based on the original recommendation. The approach is proven to
guarantee recommendations that are envy-free up to one item (EF1) (Budish,
2011). The subsequent work by Biswas et al (2021) improves the model by
identifying and removing envy-circles, which are directed cycles in a graph
representation of user envy, without affecting the EF1 guarantee. Patro et al
(2020b) look into incrementally updating the recommendation according to new
data or major changes while retaining user and provider-side fairness. They
consider three scenarios: switching the underlying recommender system,
incorporating new data, and considering additional features in relevance
estimation. For this approach, user-side fairness is the primary goal, and its
performance is enforced through constraints in the proposed integer linear
programming approach.

Similarly, Do et al (2021) also optimizes consumer- and provider-side fairness
with respect to custom utility measures based on the base recommender’s
predictions and ranking exposure. Their key insight is to consider the utility
of each user and item an objective, but ordering the objectives by performance
for Pareto efficiency comparisons, e.g., the utility of users $u_{1}$ and
$u_{3}$ are compared if they achieve the worst utilities in the two compared
solutions. This objective formulation and ordering render Pareto efficiency
equivalent to Lorenz efficiency, meaning that the utility of the worse-off
users and items is maximized, and the model is optimized using the Frank-Wolfe
algorithm.

Wu et al (2021c) considers a similar two-sided setting as the work above but
opens for providers having more than one item each. Further, the provider
exposure is not considered uniform across recommendation ranks but higher in
better positions on the recommended lists. For each recommendation position,
the approach iterates through the users in an order based on the current
recommendation utility and attempts to fill the position with a high-ranking
item in the user’s original recommendation, subject to maximum restrictions on
provider exposure. Unfilled positions are since filled with items for meeting
exposure requirements.

Another two-sided approach is found in Wu et al (2022a), which differs from
the aforementioned two-sided approaches by relying more heavily on established
optimization models. The consumer-side fairness objective is set to minimize
the variance of smooth, i.e., differentiable, NDCG. In contrast, the provider-
side fairness objective similarly considers the variance of exposure achieved
by different items. The setup is applied by considering the base
recommendation of multiple models, including two matrix factorization models
and one neural collaborative filtering model, and produces multiple Pareto
optimal solutions. The final solution is selected among these by favouring the
solution that yields the best outcome for the worst-off objective. Thus,
unlike Patro et al (2020a); Wu et al (2021c) whose methods prioritized
provide- and consumer-side fairness, respectively, through the order in which
the objectives were considered, this approach does not explicitly favour one
objective.

####  6.2.3 Classification methods

A return to matchmaking recommender systems is found in Paraschakis and
Nilsson (2020), which details a calibration-based fairness approach. The
approach considers the case where users define their preference for dating
within their race or religion on a percentage scale, and the fairness
objective is defined as making sure that the recommended list of each user has
a racial or religious composition close to their preference. One proposed way
to model the fair recommendation problem is to frame it as a Knapsack problem
and find optimal solutions using dynamic programming. They also propose an
alternative Tabu-search-based approach, which scales better but does not
guarantee an optimal solution. The fairness evaluation is based on the same
calibration applied throughout the approach as a fairness definition.

##  7 Metrics

A plethora of different metrics have been proposed and applied in the
identified research. Contributing factors to this great number of metrics are
varying fairness definitions and the fact that different recommender system
settings pose different requirements, e.g., rating vs ranking, binary vs
multivalent sensitive attributes, and user-item vs user-user recommender
systems. Another significant factor is how recently the topic has become
relevant and the subsequent lack of consensus regarding evaluation. The
metrics have all been structured according to the fairness categories they
adhere to, and liberties have been taken in grouping similar metrics under new
descriptive names. Further, formulas have been adapted and rewritten in the
same notation for consistency. A lookup table for said notation can be found
in Table 1. Finally, each subsection covers a Fairness Interpretation and
presents a table of the identified metrics, key contexts, and a list of the
research that applied them.

###  7.1 Recommendation Parity Metrics

Table 7: Overview of identified Recommendation Parity metrics, their key properties and the research that has applied them. Name |  Fairness Subcategory |  Sensitive Attribute |  Rec. Dynamic |  Rec. Type |  Research
---|---|---|---|---|---
Item-level Parity |  Local Parity |  Binary111Binary definition has also been applied to multivalent settings by applying it for all possible pairs. |  User-Item |  Mixed |  Bose and Hamilton (2019)
Islam et al (2021)
Frisch et al (2021)
Wu et al (2021b)
Item-level Rating Deviation |  Local Parity |  Multivalent |  User-Item |  Ranking |  Xu et al (2021)
Global-level Parity |  Global Parity |  Binary |  User-Item |  Rating |  Yao and Huang (2017)
Farnadi et al (2018)
Dickens et al (2020)
Ashokan and Haas (2021)
Fang et al (2022)
Rus et al (2022)
Mutual Information, Rating |  Global Parity |  Binary |  User-Item |  Rating |  Kamishima et al (2012)
Kamishima et al (2013)
Kolmogorov-Smirnov |  Global Parity |  Binary |  User-Item |  Mixed |  Kamishima et al (2016)
Kamishima and Akaho (2017)
Kamishima et al (2018)
$\chi^{2}\text{-test}$ |  Local Parity |  Binary |  User-item |  Ranking |  Frisch et al (2021)
Group-to-group Variance |  Global Parity |  Multivalent |  User-User |  Ranking |  Rahman et al (2019)
Buyl and Bie (2020)
Sensitive-group Share |  Global Parity |  Multivalent |  User-User |  Ranking |  Rahman et al (2019)

####  7.1.1 Item-level Parity

Three identified metrics share a general design for summarizing the disparity
of ratings or recommendations at the item level. All three metrics measure the
item-level difference of ratings/recommendations aggregated by sensitive
groups and a final aggregation by items.

$\hat{\mathbb{E}}_{v\in\mathcal{V}}\bigl{[}\arrowvert\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{1}}}[\hat{r}_{uv}]-\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{2}}}[\hat{r}_{uv}]\arrowvert\bigl{]}$

Bose and Hamilton (2019); Wu et al (2021b) apply identical metrics that
consider the simple absolute difference of item ratings for different groups
in binary-sensitive attribute settings. Bose and Hamilton (2019) also consider
multivalent sensitive attributes, for which Equation 7.1.1 is expanded to
consider all possible pairs of sensitive groups.

$\hat{\mathbb{E}}_{v\in\mathcal{V}}\left[\left\arrowvert\ln{\left(\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{1}}}\left[1\\{\hat{y}_{uv}\\}\right]\right)}-\ln{\left(\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{2}}}\left[1\\{\hat{y}_{uv}\\}\right]\right)}\right\arrowvert\right]\\\
$ (1)

$\max_{v1,v2\in\mathcal{V}\arrowvert v1\neq
v2}\left\arrowvert\left(\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{1}}}\left[1\\{\hat{r}_{uv_{1}}>\hat{r}_{uv_{2}}\\}\right]\right)-\left(\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{2}}}\left[1\\{\hat{r}_{uv_{1}}>\hat{r}_{uv_{2}}\\}\right]\right)\right\arrowvert\\\
$ (2)

Islam et al (2021); Frisch et al (2021) both define similar concepts named
$\epsilon$-(differentially)fair, where individual $\epsilon$’s reflect how
much the recommendation of a single item differs in a binary sensitive group
setting. The former considers the probability of recommending items to
different sensitive groups, Equation 1, while the latter considers the
probability of ranking an item higher than another item to different sensitive
groups, Equation 2. Islam et al (2021) takes inspiration from differential
privacy (Dwork, 2011), and subsequently have logarithmic terms in the absolute
difference, but opt for computing the average $\epsilon$ and not the maximum.
Frisch et al (2021) does not cite differential metrics or concepts, but is
concerned with the maximum $\epsilon$ and not the average. Out of the two
aggregations, the maximum poses a stronger guarantee than the average and is
more in line with the differential definition.

####  7.1.2 Item-level Rating Deviation

$\displaystyle\hat{\mathbb{E}}_{v\in\mathcal{V}}\sqrt{\hat{\mathbb{E}}_{j\in\mathcal{S}}\left[\left(\hat{\mathbb{E}}_{u\in\mathcal{U}_{j}}[\hat{r}_{uv}]-\mu_{v}\right)^{2}\right]},$
$\displaystyle\text{where
}\mu_{v}=\hat{\mathbb{E}}_{k\in\mathcal{S}}\bigl{[}\hat{\mathbb{E}}_{u\in
U_{k}}[\hat{r}_{uv}]\bigl{]}.$

While the Item-level Parity metrics consider the mean difference of predicted
item ratings between sensitive groups, Xu et al (2021) opt for measuring the
mean standard deviation of the same ratings. The metric is inherently capable
of considering more than two sensitive groups, and the square difference term
leads to larger penalties for large differences than the corresponding
penalties in the metrics applying the absolute difference instead.

####  7.1.3 Global-level Parity

$\left\arrowvert\hat{\mathbb{E}}_{v\in\mathcal{V}}\left[\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{1}}}\left[\hat{r}_{uv}\right]\right]-\hat{\mathbb{E}}_{v\in\mathcal{V}}\left[\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{2}}}\left[\hat{r}_{uv}\right]\right]\right\arrowvert$

The Global-level Parity metric is applied in multiple research and is simply
the absolute difference of the mean predicted rating or preference score of
different sensitive groups.

####  7.1.4 Mutual Information, Rating

$\sum_{s\in\mathcal{S}}\int\text{P}(\hat{r},s)\log\frac{\text{P}(\hat{r}\arrowvert
s)}{\text{P}(\hat{r})}d\hat{r}$

Mutual information is a concept from information theory, comprising a measure
of the mutual dependency of two variables. It has been applied in fair
recommender systems to measure the mutual dependency of the rating and the
sensitive attribute. Due to the probabilistic definition, non-probabilistic
models applying the metric have resorted to different methods for
approximating the measure, e.g., empiric approximations of probabilities and
bucketing the ratings into intervals to replace the inner integral with a sum.

####  7.1.5 Kolmogorov-Smirnov Statistic

$\sup_{\hat{r}}\arrowvert F_{s_{1}}(\hat{r})-F_{s_{2}}(\hat{r})\arrowvert$

The Kolmogorov-Smirnov(KS) statistic measures how different two probability
distributions are, and its estimation involves the cumulative distributions of
the probability distributions. Both cumulative distributions are typically
empirically defined based on the outputted ratings for different sensitive
groups when used in recommender systems. $\sup$ is the supremum, meaning that
the statistic returns the upper-bounded difference between the distributions
of the ratings.

####  7.1.6 $\chi^{2}$-Test

$\chi^{2}$-tests are typically used to determine if the difference in
collections of categorical data is probable, given that they were sampled from
the same distribution. Frisch et al (2021) applied $\chi^{2}$-test to test the
independence of group membership and user gender. Since group membership
influences the rating within their Latent Block Model, the groups’ gender
composition should ideally reflect the overall gender composition when
pursuing recommendation parity.

####  7.1.7 Group-to-group Variance

$\displaystyle\hat{\mathbb{E}}_{a,b\in\mathcal{S}\times\mathcal{S}\arrowvert
a\neq b}[($ $\displaystyle N_{a}-N_{b})^{2}],$ where $\displaystyle
N_{a}=N_{s_{i},s_{j}}=\frac{\arrowvert\\{\hat{y}_{u_{1},u_{2}}\arrowvert
u_{1}\in\mathcal{U}_{s_{i}},u_{2}\in\mathcal{U}_{s_{j}}\\}\arrowvert}{\arrowvert\mathcal{U}_{s_{i}}\times\mathcal{U}_{s_{j}}\arrowvert}.$

In reciprocal recommendations, each recommendation involves two users who may
belong to different sensitive groups. The Group-to-group Variance metric
considers the variance of the acceptance rate, i.e., recommendation rate, of
different combinations of sensitive groups.

####  7.1.8 Sensitive-group Share

$\mathcal{S}\text{-share}(s)=\frac{1}{\arrowvert\mathcal{S}\arrowvert}-\frac{\sum_{u_{1}\in\mathcal{U}}\sum_{u_{2}\in\mathcal{U}_{s}}\frac{1\\{u_{2}\in\text{Rec}_{u_{1}}\\}}{\arrowvert\text{Rec}_{u_{1}}\arrowvert}}{\arrowvert\mathcal{U}\arrowvert}$

The Sensitive-group Share metric measures how well an individual sensitive
group $s$ is represented in the recommendations of all users in a reciprocal
setting. It subtracts the real representation ratio for said group from the
ideal uniform ratio, such that the output represents how far from ideal the
recommendations are with respect to single sensitive groups.

###  7.2 Neutral Representation Metrics

Neutral Representation fairness is a special case in that it does not
explicitly concern itself with the actual outputs of the model. This also
extends to the metrics of the Fairness Interpretation. However, while some
research adapting this Fairness Interpretation in their optimization only
evaluate how neutral the representations are, others adapt metrics from other
interpretations to evaluate the recommendation explicitly.

Table 8: Overview of identified Neutral Representation metrics, their key properties and the research that has applied them. Name |  Sensitive groups |  Rec. Dynamic |  Rec. Type |  Research
---|---|---|---|---
Sensitive Reclassification |  Multivalent |  Mixed |  Mixed |  Bose and Hamilton (2019)
Resheff et al (2019)
Buyl and Bie (2020)
Li et al (2021b)
Wu et al (2021b)
Li et al (2022a)
Borges and Stefanidis (2022)
Wu et al (2022b)
Wei and He (2022)

####  7.2.1 Sensitive Reclassification

The vast majority of research optimizing for sensitive neutral representations
perform some form of evaluation of how well sensitive information can be
reclassified through the representations. This evaluation is usually performed
by training an auxiliary classification model specifically for identifying the
sensitive attributes of users given their representations, and the re-
classification score becomes an inverse measure of how well sensitive
information has been eliminated. Accuracy, F1 score and Area Under the ROC
Curve(AUC) are all metrics that have been used for this purpose. AUC is the
total area under the curve of the curve you get by plotting the true positive
rate and the false positive rate while moving the threshold used to split
positive and negative classifications. AUC is by far the most applied
classification metric.

###  7.3 Utility-Based Fairness

Utility-Based fairness metrics are specifically tied to utility functions that
consider the ground truth in their definitions, i.e., the utility or utility
contribution of a single user increases if an item in the test set is
successfully recommended for said user. This covers established pure-
recommendation metrics, as well as other specialized utility measures.

Table 9: Overview of identified Utility-Based Fairness metrics, their key properties and the research that has applied them. Name |  Fairness Subcategory |  Sensitive groups |  Rec. Dynamic |  Rec. Type |  Research
---|---|---|---|---|---
Group Rating Error Difference |  Group |  Binary111Binary definition, but has also been applied to multivalent settings by taking the mean or standard deviation of all possible pairs/one-vs-all values. |  User-item |  Mixed |  Yao and Huang (2017)
Farnadi et al (2018)
Dickens et al (2020)
Islam et al (2021)
Wu et al (2021b)
Fang et al (2022)
Group Rating Error Deviation |  Group |  Multivalent |  User-item |  Mixed |  Xu et al (2021)
Group Utility Difference |  Group |  Binary111Binary definition, but has also been applied to multivalent settings by taking the mean or standard deviation of all possible pairs/one-vs-all values. |  Mixed |  Mixed |  Zheng et al (2018)
Islam et al (2019)
Huang et al (2021)
Liu et al (2022c)
Borges and Stefanidis (2022)
Liu et al (2022b)
Liu et al (2022a)
Wei and He (2022)
Utility Variance |  Mixed |  Multivalent |  User-item |  Mixed |  Rastegarpanah et al (2019)
Wu et al (2021c)
Wu et al (2022a)
Utility Delta |  Group |  Multivalent |  User-item |  Mixed |  Li et al (2021a)
Slokom et al (2021)
Mutual Information, Relevance |  Group |  Binary |  User-Item |  Ranking |  Kamishima and Akaho (2017)
Inequality of Odds |  Group |  Binary |  User-item |  Ranking |  Li et al (2022a)
Inequality of Opportunity |  Group |  Binary |  User-item |  Ranking |  Kamishima and Akaho (2017)
Protected Utility |  Group |  Binary |  User-item |  Rating |  Yao and Huang (2021)
GEI |  Group |  Binary |  User-item |  Rating |  Ashokan and Haas (2021)
Generalized Cross Entropy |  Group |  Multivalent |  User-item |  Ranking |  Liu et al (2022c)
F-Statistic Utility |  Group |  Multivalent |  User-item |  Rating |  Wan et al (2020)

####  7.3.1 Group Rating Error Difference

$\displaystyle\text{ValueUnfairness}=$
$\displaystyle\phantom{===}\hat{\mathbb{E}}_{v\in\mathcal{V}}\left[\biggl{\arrowvert}\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{1}}}[\hat{r}_{uv}-r_{uv}]-\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{2}}}[\hat{r}_{uv}-r_{uv}]\biggl{\arrowvert}\right]$
(3) $\displaystyle\text{AbsoluteUnfairness}=$
$\displaystyle\phantom{===}\hat{\mathbb{E}}_{v\in\mathcal{V}}\left[\biggl{\arrowvert}\Bigl{\arrowvert}\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{1}}}[\hat{r}_{uv}-r_{uv}]\Bigl{\arrowvert}-\Bigl{\arrowvert}\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{2}}}[\hat{r}_{uv}-r_{uv}]\Bigl{\arrowvert}\biggl{\arrowvert}\right]$
(4) $\displaystyle\text{OverestimationUnfairness}=$
$\displaystyle\phantom{===}\hat{\mathbb{E}}_{v\in\mathcal{V}}\left[\biggl{\arrowvert}\max\Bigl{(}0,\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{1}}}[\hat{r}_{uv}-r_{uv}]\Bigl{)}-\max\Bigl{(}0,\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{2}}}[\hat{r}_{uv}-r_{uv}]\Bigl{)}\biggl{\arrowvert}\right]$
$\displaystyle\text{UnderestimationUnfairness}=$
$\displaystyle\phantom{===}\hat{\mathbb{E}}_{v\in\mathcal{V}}\left[\biggl{\arrowvert}\max\Bigl{(}0,\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{1}}}[r_{uv}-\hat{r}_{uv}]\Bigl{)}-\max\Bigl{(}0,\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{2}}}[r_{uv}-\hat{r}_{uv}]\Bigl{)}\biggl{\arrowvert}\right]$

These four metrics were all defined by Yao and Huang (2017) and make out some
of the few metrics that have gained a semblance of recognition in subsequent
work on consumer-side recommendation fairness. Every metric accumulates
absolute differences in per-item errors of two sensitive groups, and all of
them involve mechanics for cancelling errors in case the model is similarly
underperforming for both groups. The latter two focus on over- and under-
estimation, respectively, while the former two consider both error types
concurrently while differing in how the errors can cancel out. Specifically,
Value Unfairness, Equation 3, allows errors of the same type to cancel out,
while Absolute Unfairness, Equation 4, allows all errors to cancel out
regardless of error type.

$\hat{\mathbb{E}}_{v\in\mathcal{V}}\left[\biggl{\arrowvert}\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{1}}}\Bigl{[}\arrowvert\hat{r}_{uv}-r_{uv}\arrowvert\Bigl{]}-\hat{\mathbb{E}}_{u\in\mathcal{U}_{s_{2}}}\Bigl{[}\arrowvert\hat{r}_{uv}-r_{uv}\arrowvert\Bigl{]}\biggl{\arrowvert}\right]\\\
$ (5)

The metric applied in Wu et al (2021b) resembles Absolute Unfairness, but
considers the absolute errors at the user level instead of at the group level.
One implication of this is a higher incurred penalty when the errors of the
predicted ratings vary a lot within one or both groups, as they are not evened
out by taking the group-wise mean before the absolute error is calculated,
which is the case for Absolute Unfairness.

####  7.3.2 Group Rating Error Deviation

$\displaystyle\hat{\mathbb{E}}_{v\in\mathcal{V}}\left[\sqrt{\hat{\mathbb{E}}_{i\in\mathcal{S}}\left[\left(\hat{\mathbb{E}}_{u\in\mathcal{U}_{i}}\left[\arrowvert\hat{r}_{uv}-r_{uv}\arrowvert\right]-\mu_{v}\right)^{2}\right]}\right],$
$\displaystyle\text{where }\mu_{v}=\hat{\mathbb{E}}_{j\in
S}\left[\left(\hat{\mathbb{E}}_{u\in
U_{j}}\left[\arrowvert\hat{r}_{uv}-r_{uv}\arrowvert\right]\right)\right].$

Along with Item-level Rating Deviation, Xu et al (2021) propose another metric
that considers the standard deviation of item-level statistics of different
sensitive groups. This time, it is a Utility-Based fairness metric, with a
central term considering the squared difference of mean user-level absolute
item rating errors. While the metric is structurally similar to Group Rating
Error, see in particular Equation 5, it is important to note that this metric
measures the mean standard deviation of the group-wise rating errors instead
of the mean difference of the same errors. Further, the Group Rating Error
Deviation metric is inherently capable of considering multivalent sensitive
attributes.

####  7.3.3 Group Utility Difference

$\arrowvert\text{Util}(\mathcal{U}_{s_{1}})-\text{Util}(\mathcal{U}_{s_{2}})\arrowvert$

Among the considered research, some explicitly calculate the absolute
difference of Recall, Precision and NDCG (Järvelin and Kekäläinen, 2002)
achieved by different sensitive groups. Also included in this group of metrics
are more implicit comparisons of utility metrics through tables or graphs,
which has been observed considering MAE, cumulative mean custom rewards and
custom matchmaking utility. A special case of this metric is applied in the
reciprocal setting of Zheng et al (2018), where the users receiving the
recommendation comprise one sensitive group, and the users that make up the
recommended entities comprise the other sensitive group.

####  7.3.4 Utility Variance

$\displaystyle\hat{\mathbb{E}}_{u_{1}\in\mathcal{U}}\left[\hat{\mathbb{E}}_{u_{2}\in\mathcal{U}\arrowvert
u_{2}\neq
u_{1}}\left[(\text{Util}(u_{1})-\text{Util}(u_{2}))^{2}\right]\right]$
$\displaystyle\hat{\mathbb{E}}_{s_{1}\in\mathcal{S}}\left[\hat{\mathbb{E}}_{s_{2}\in\mathcal{S}\arrowvert
s_{2}\neq
s_{1}}\left[(\text{Util}(\mathcal{U}_{s_{1}})-\text{Util}(\mathcal{U}_{s_{2}}))^{2}\right]\right]$

The variation of the utility of individual users or sensitive groups has been
applied as fairness metrics. It is particularly suited for representing the
utility spread when there are too many scores to cover individually, i.e.,
many users or sensitive groups. The identified variations of Utility Variance
have centred around the utility metrics Mean Squared Error and NDCG.

####  7.3.5 Utility Delta

$\displaystyle\Delta_{s}$
$\displaystyle=\text{Util}(\mathcal{U}_{s})-\text{Util}_{\text{org}}(\mathcal{U}_{s})$
$\displaystyle\Delta_{\text{diff}}$
$\displaystyle=\arrowvert\Delta_{s_{1}}-\Delta_{s_{2}}\arrowvert$ (6)

The Utility Delta metrics consider how the utility of specific sensitive
groups changes when a fairness-aware model is compared to baselines. From a
Utility-Based fairness view, a decrease in utility for a dominant sensitive
group may be worth a subsequent increase in the utility of worse-off sensitive
groups. Having measures of how the utility of specific user groups has changed
is useful when considering such trade-offs. Slokom et al (2021) also consider
the absolute difference of the $\Delta$-s of two sensitive groups to capture
the dissymmetry in the magnitude of the changes, Equation 6.

####  7.3.6 Mutual Information, Relevance

Kamishima and Akaho (2017) applies mutual information in a Utility-Based
fairness evaluation of their ranking-based recommender system. The definition
is structurally identical to that of the Recommendation Parity metric in
Section 7.1.4. The main difference is that the predicted rating variable is
replaced with a binary relevancy variable, i.e., the degree of independence
between relevant recommendations and the sensitive attribute is measured.

####  7.3.7 Inequality of Odds

$\max(\arrowvert\text{FPR}_{s_{1}}-\text{FPR}_{s_{2}}\arrowvert,\arrowvert\text{TPR}_{s_{1}}-\text{TPR}_{s_{2}}\arrowvert)$

Equality of Odds requires the true positive and false positive rates of
different sensitive groups to be equal. Li et al (2022a) propose a metric
based on this definition for measuring the extent of potential infractions.
The same research also applies Absolute Between-ROC Area(ABROCA), proposed in
Gardner et al (2019), which inherently considers all possible positive-
boundary thresholds as opposed to a single fixed threshold.

####  7.3.8 Inequality of Opportunity

$\text{TPR}_{s_{1}}-\text{TPR}_{s_{2}}$

Kamishima and Akaho (2017) considers a metric based on Equality of
Opportunity, which requires equality of true positive rates of different
sensitive groups. They opt for measuring infractions with a regular difference
to avoid abstracting away the orientation of potential imbalances.

####  7.3.9 Protected Utility

The protected utility metrics only consider the utility of specific sensitive
groups that are considered protected. Yao and Huang (2021) is the only
identified research that adopts this metric type, and they use RMSE as their
utility measure.

####  7.3.10 Generalized Entropy Index

$\text{GEI}(\alpha)=\begin{cases}\frac{1}{\arrowvert\mathcal{S}\arrowvert\alpha(1-\alpha)}\sum_{s\in\mathcal{S}}\left(\left(\frac{\text{Util}(\mathcal{U}_{s})}{\text{Util}(\mathcal{U})}\right)^{\alpha}-1\right),&\alpha\neq
0,1\\\
\frac{1}{\arrowvert\mathcal{S}\arrowvert}\sum_{s\in\mathcal{S}}\frac{\text{Util}(\mathcal{U}_{s})}{\text{Util}(\mathcal{U})}\ln\frac{\text{Util}(\mathcal{U}_{s})}{\text{Util}(\mathcal{U})},&\alpha=1\\\
-\frac{1}{\arrowvert\mathcal{S}\arrowvert}\sum_{s\in\mathcal{S}}\ln\frac{\text{Util}(\mathcal{U}_{s})}{\text{Util}(\mathcal{U})},&\alpha=0\\\
\end{cases}$

Generalized Entropy Index(GEI) is a metric often used for measuring income
inequality and has been applied both for measuring individual inequality and
inequality among larger user groups in recommender systems. In the case of GEI
based on individuals, $s$ is interpreted as each user having their own
sensitive group $\mathcal{U}_{s}$. Note that the applied utility measure
typically will average over all represented users to get comparative scores
when calculating the utility of all users and the one based on a subset of the
users. Farnadi et al (2018) consider GEI for both $\alpha=1$ and $\alpha=2$,
where the former yields a special case known as the Theil index.

####  7.3.11 Generalized Cross Entropy

$\text{GCE}(m,S)=\frac{1}{\beta\cdot(1-\beta)}\left(\sum_{s\in
S}\text{P}_{f}^{\beta}(s)\cdot\text{P}_{m}^{(1-\beta)}(s)-1\right)$

Generalized Cross Entropy allows the evaluator to adjust the importance given
to the utility of different sensitive groups, e.g., in settings where you have
premium users or known marginalized users for whom one wants to boost the
performance. $\text{P}_{f}$ is a fair probability distribution, e.g., a
uniform distribution if the motive is to give equal focus to all sensitive
groups. $\text{P}_{m}$ is a probability distribution over the model $m$’s
utility.

####  7.3.12 $F$-Statistic

The $F$-Statistic is typically calculated as part of a $F$-test used in
analyses of variance. Wan et al (2020) applies the $F$-statistic while
considering the variance of rating errors between market segments and within
them as a measure of fairness, where lower $F$-statistics indicate higher
levels of fairness.

###  7.4 Custom Fairness

Custom fairness encompasses all definitions and measures that do not strictly
consider Recommendation Parity, representation neutrality or Utility-Based
fairness. Unlike Utility-Based fairness metrics, any utility considered in
these metrics is not affected by the ground truth. Additionally, while some of
these metrics consider parity-based concepts, it concerns aspects other than
recommendation, i.e., not explicitly rating, preference or ranking. For
instance, parity with respect to derived/contextual user attributes or a
particular item group.

Table 10: Overview of identified Custom fairness metrics, their key properties and the research that has applied them. |  Sensitive groups |  Rec. Dynamic |  Rec. Type |  Research
---|---|---|---|---
Normalized Ranking Change |  Multivalent |  User-item |  Ranking |  Patro et al (2020a)
Patro et al (2020b)
Biswas et al (2021)
Ranking Change Envy |  Multivalent |  User-item |  Ranking |  Patro et al (2020a)
Biswas et al (2021)
Gini Coefficient, Preference |  Multivalent |  Mixed |  Ranking |  Do et al (2021)
Protected Item-group Recommendation Parity |  Binary |  User-item |  Ranking |  Burke et al (2018)
Preferential Calibration |  Multivalent |  User-item |  Ranking |  Paraschakis and Nilsson (2020)
Intrinsic Sensitive Attribute Match |  Binary |  User-item |  Ranking |  Bobadilla et al (2021)
Sensitive Neutral Recommended Items |  Multivalent |  User-item |  Ranking |  Li et al (2022b)
Segment Recommendation Frequency Parity |  Multivalent |  User-item |  Ranking |  Wan et al (2020)
Sensitive Reclassification, Pre-/Post- |  Multivalent |  User-item |  Mixed |  Edizel et al (2020)
Wu et al (2021a)
Slokom et al (2021)

####  7.4.1 Normalized Ranking Change

$\displaystyle\text{PrefUtil}_{u}$
$\displaystyle(\text{Rec})=\frac{\sum_{v\in\text{Rec}}\text{pref}_{uv}}{\sum_{v^{\prime}\in\text{Rec}_{\text{org\\_u}}}\text{pref}_{uv^{\prime}}}$
(7) NormRankChg
$\displaystyle\text{Mean}=\hat{\mathbb{E}}_{u\in\mathcal{U}}\left[\text{PrefUtil}_{u}(\text{Rec}_{u})\right]$
NormRankC $\displaystyle\text{hgStd}=$
$\displaystyle\sqrt{\hat{\mathbb{E}}_{u_{1}\in\mathcal{U}}\left[\hat{\mathbb{E}}_{u_{2}\neq
u_{1}}\left[\left(\text{PrefUtil}_{u_{1}}(\text{Rec}_{u_{1}})-\text{PrefUtil}_{u_{2}}(\text{Rec}_{u_{2}})\right)^{2}\right]\right]}$

Patro et al (2020a, b); Biswas et al (2021) all consider a two-sided fairness
setting and interpret the consumer-side fairness as how far the
recommendations deviate from the original ranking when producer-side fairness
has been taken into account. I.e., they use the intermediate preference scores
of the re-ranked top-$k$ recommendations normalized by the optimal preference
scores of the original top-$k$ recommendations as a proxy of the utility. This
utility’s mean and standard deviation are considered in their fairness
evaluation.

####  7.4.2 Ranking Change Envy

$\displaystyle\text{RankingEnvy}(u,u^{\prime})$
$\displaystyle=\max(\text{PrefUtil}_{u}(\text{Rec}_{u^{\prime}})-\text{PrefUtil}_{u}(\text{Rec}_{u}),0)$
RankChgEnvy
$\displaystyle=\hat{\mathbb{E}}_{u_{1}\in\mathcal{U}}\left[\hat{\mathbb{E}}_{u_{2}\neq
u_{1}}\left[\text{RankingEnvy}(u_{1},u_{2})\right]\right]$

In multi-sided fairness settings, it is not uncommon to have a situation where
the utility of one user may be increased by giving said users the
recommendations given to another user instead of their own. The term Envy has
been taken to refer to cases where users would fare better given the
recommendations of other users. Envy can arise in multi-sided
recommendendation fairness when auxiliary considerations affect some users
more than others, e.g., considerations of provider-side fairness. Patro et al
(2020a) and Biswas et al (2021) consider the aggregated envy of their proposed
preference utility, Equation 7.

####  7.4.3 Gini Coefficient, Preference

$\displaystyle\text{PrefUtilExp}(u)$
$\displaystyle=\sum_{v\in\mathcal{V}}\text{pref}_{uv}\boldsymbol{P}_{uv}\boldsymbol{w}$
(8) GiniPref
$\displaystyle=\frac{\sum_{u_{1},u_{2}\in\mathcal{U}\times\mathcal{U}}\arrowvert\text{PrefUtilExp}(u_{1})-\text{PrefUtilExp}(u_{2})\arrowvert}{2\arrowvert\mathcal{U}\arrowvert^{2}\mathbb{E}_{u\in\mathcal{U}}[\text{PrefUtilExp}(u)]}$

Do et al (2021) propose adapting the Gini coefficient, frequently used to
measure wealth inequality, to measure individual consumer fairness in their
two-sided fairness setting. The Gini coefficient is measured for a custom
utility measure based on the outputted preference scores of their base
recommender system and the ranking positions of the re-ranked recommendations.
Their proposed utility measure is defined in Equation 8, where
$\boldsymbol{P_{uv}}$ is a row vector of probabilities for recommending user
$u$ item $v$ in different ranking positions, and $\boldsymbol{w}$ is a column
vector of exposure/rank weights for the same ranking positions.

####  7.4.4 Protected Item-group Recommendation Parity

$\frac{\sum_{u\in\mathcal{U}_{s_{1}}}\sum_{v\in\text{Rec}_{u}}\frac{\gamma(v)}{\arrowvert\mathcal{U}_{s_{1}}\arrowvert}}{\sum_{u^{\prime}\in\mathcal{U}_{s_{2}}}\sum_{v^{\prime}\in\text{Rec}_{u^{\prime}}}\frac{\gamma(v^{\prime})}{\arrowvert\mathcal{U}_{s_{2}}\arrowvert}}$

Here $\gamma$ is a function that returns “1” if the item belongs to any
protected item groups and “0” if none of its item groups is protected, and the
metric measures how balanced the recommendation of the protected item groups
are between two sensitive groups, i.e., a value of 1 is optimal. Burke et al
(2018) applied this metric to evaluate their method’s fairness on a film
dataset and a micro-loan dataset. The protected item groups were selected
among film genres that are unevenly recommended to different genders for the
film dataset, and among the most unfunded regions in the micro-loan dataset.

####  7.4.5 Preferential Calibration

$1-\frac{\delta_{u}-\delta_{\text{min}\\_u}}{\delta_{\text{max}\\_u}-\delta_{\text{min}\\_u}}$

Paraschakis and Nilsson (2020) consider a matchmaking scenario where users can
set their preference for being matched with people belonging to the same
sensitive group as them. The proposed metric measures how well the provided
recommendation respects the user’s preferences, a concept known as calibrated
recommendation (Steck, 2018). First, the optimal recommendation composition is
calculated based on the provided user preference and the sensitive group
composition of the full population. $\delta_{u}$ is then calculated as the
absolute difference between the ideal and actual composition. Finally, the
normalized $\delta$ is subtracted from 1 after identifying the best and worst
possible $\delta$-s for the actual user, yielding a metric for which values
closer to 1 indicate that the users’ preferences are better respected.

####  7.4.6 Intrinsic Sensitive Attribute Match

$\text{IntrinsicSensitiveMatch}(u,v)=(\text{UserIntrinsic}_{u}-\text{ItemIntrinsic}_{v})^{2}$

Bobadilla et al (2021) devise a notion of intrinsic sensitive properties in
both items and users. They assign values to the said property for items by
first considering the ratio of female users who like the items compared to the
ratio of female users who dislike them, then taking the difference between
that value and the equivalent value calculated for male users. These item
values are then used reversely to assign values to the same intrinsic
properties of the individual users. The fairness of the individual
recommendations is set to be the squared difference between the intrinsic user
value and the intrinsic item value.

####  7.4.7 Sensitive Neutral Recommended Items

$\displaystyle\text{IF}(u)$
$\displaystyle=\sum_{v\in\text{Rec}_{u}}\text{SensitiveEntropy}_{v}$
$\displaystyle\text{DIF}(u)$
$\displaystyle=\text{IF}(u)-\text{IF}_{\text{ground\\_truth}}(u),$