# Cross-domain User Preference Learning for Cold-start Recommendation

Huiling Zhou*, Jie Liu*, Zhikang Li*, Jin Yu, Hongxia Yang  zhule.zhl,
sanshuai.lj, zhikang.lzk, kola.yu<EMAIL_ADDRESS>DAMO Academy,
Alibaba GroupChina

###### Abstract.

Cross-domain cold-start recommendation is an increasingly emerging issue for
recommender systems. Existing works mainly focus on solving either cross-
domain user recommendation or cold-start content recommendation. However, when
a new domain evolves at its early stage, it has potential users similar to the
source domain but with much fewer interactions. It is critical to learn a
user’s preference from the source domain and transfer it into the target
domain, especially on the newly arriving contents with limited user feedback.
To bridge this gap, we propose a self-trained Cross-dOmain User Preference
LEarning (COUPLE) framework, targeting cold-start recommendation with various
semantic tags, such as attributes of items or genres of videos. More
specifically, we consider three levels of preferences, including user history,
user content and user group to provide reliable recommendation. With user
history represented by a domain-aware sequential model, a frequency encoder is
applied to the underlying tags for user content preference learning. Then, a
hierarchical memory tree with orthogonal node representation is proposed to
further generalize user group preference across domains. The whole framework
updates in a contrastive way with a First-In-First-Out (FIFO) queue to obtain
more distinctive representations. Extensive experiments on two datasets
demonstrate the efficiency of COUPLE in both user and content cold-start
situations. By deploying an online A/B test for a week, we show that the
Click-Through-Rate (CTR) of COUPLE is superior to other baselines used on
Taobao APP. Now the method is serving online for the cross-domain cold micro-
video recommendation.

cross-domain, cold-start recommendation, user preference learning

*These authors contributed equally to this research.

††ccs: Computer systems organization Embedded systems††ccs: Computer systems
organization Redundancy††ccs: Computer systems organization Robotics††ccs:
Networks Network reliability

##  1\. Introduction

Figure 1. Overview of the proposed cross-domain cold-start recommendation
system. A user’s preference is captured from different perspectives with
jointly modeling behaviors in all domains.

Personalized recommendation system (RS) plays a vital role in an e-commerce
platform, where effective strategies have been made to alleviate information
overload and facilitate better user experiences. In recent years, deep
learning has been widely applied in RS to overcome obstacles of conventional
recommendation techniques. Great effort has been made to achieve better
performances in heterogeneous multi-modal recommendation (Geng et al., 2015;
Epasto and Perozzi, 2019; Pal et al., 2020), debiased recommendation (Guo et
al., 2020; Zhou et al., 2020), reliable and explainable recommendation (Wang
et al., 2019; Chen et al., 2020), etc. Among all, cross-domain recommendation
(Elkahky et al., 2015; Hu et al., 2018; Zhao et al., 2020) and cold-start
recommendation (Li et al., 2019a; Cohen et al., 2017; Lu et al., 2020)
problems draw a lot of attention. Cross-domain recommendation systems aim to
transfer knowledge available in other domains (known as the source domain) to
the target domain where users have much sparser feedback or interactions.
Overlapped users are often selected to learn the mapping of interest between
two domains so that same pattern can be applied to those cold-start users of
target domain (Hu et al., 2018; Zhao et al., 2020). On the other hand, cold-
start recommendation is often referred to cold-start content recommendation
where no or few user feedback can be found when new items arrive. It is
challenging to recommend such items to users due to the unavailability of the
statistical information which RS relies heavily on. Common solutions extract
and analyze content information of items to match users’ potential interests
based on their historical behaviors (Cohen et al., 2017; Geng et al., 2015).

Previous works normally treat cold-start user and cold-start content
recommendation as two separate scenarios. However, when a new domain evolves
at its early stage in real-world, it may suffer both issues at the same time.
For example, Taobao is the largest e-commerce platform in China where billions
of products are interacted with hundreds of millions of users each day. When
micro-videos were first served to the platform, they shared the same set of
users as product domain but had few (or none) user interactions. How to
perform reliable recommendation on such emerging new contents appears to be
one of the most challenging problems for RS. A recent work (Xie et al., 2020)
proposes an internal contextual attention network to deal with the cross-
domain cold-start recommendation on contents with very few interactions.
However, this approach has limited ability to model brand new contents which
are never seen before.

In this paper, we further extend the work (Xie et al., 2020) and provide a
unified Cross-dOmain User Preference LEarning (COUPLE) framework where items
with limited interactions can be reliably recommended. COUPLE differs from
previous cross-domain works in that we jointly model all users’ behaviors
across domains instead of using just the overlapped users, as shown in
Figure.1. With historical feedback modeled, a user’s preference across domains
is obtained from content perspective and user group perspective. When a new
item comes, we push it to the corresponding users with matched interest based
on its content feature and the user’s general preference learnt by the system.
Main contributions of our proposed work are summarized as follows:

  * •

We propose a unified user preference learning framework to solve cross-domain
cold-start problem, which delicately models a user’s history preference,
content preference and group preference. With proper choice of a First-In-
First-Out (FIFO) queue, the whole framework can be self-trained in an
efficient contrastive way.

  * •

With semantic tags extracted for item representation, a frequency encoder
based on cross-layer attention is utilized. It further boosts the interactions
between high-level representation with low-level content source input. To the
best of our knowledge, it is the pioneering work to solve the cross-domain
cold-start issue with the use of tag information.

  * •

A hierarchical memory tree with orthogonality property is proposed to learn
users’ preference across domains. It can generalize user’s diverse interest
with top $K$ leaf-node representations based on his/her historical behaviors.
This is proved to be a good way of user preference generalization in cross-
domain scenario.

The rest of the paper is organized as follows. In Section 2, we review the
related work. Section 3 presents the details of our proposed method. Offline
experimental results and ablation study are presented in Section 4. We
introduce the online deployment of the system in Section 5 and conclude our
work in Section 6.

##  2\. Related Work

In this section, we introduce the related work on personalized recommendation
system, user preference learning, and the orthogonal regularization mechanism
we use in the paper.

###  2.1. Personalized Recommendation System

A standard matching (i.e. candidate generation) stage of a personalized
recommender system aims to retrieve a small subset of items from the huge pool
for the sophisticated ranking scheme. Previous methods typically employ
collaborative filtering (CF) strategies to exploit user preferences from their
explicit or implicit feedback (Hu et al., 2008; He et al., 2017). These
methods achieve good performance where user-item interactions are dense but
are not able to handle the cold-start situations where the interactions are
limited. Content-based methods alleviate this problem by mining the content
features of items or meta information about users (Melville et al., 2002; Geng
et al., 2015; Epasto and Perozzi, 2019; Haruna et al., 2017; Gedikli and
Jannach, 2013). Among them, tags are proved to be useful (Gedikli and Jannach,
2013; Haruna et al., 2017), especially for cross-domain recommendation where
semantically similar tags may exist in both domains and bridge the gap to some
extent. Despite their success, both types of the methods treat user-item
interactions in a static way and cannot capture the dynamic interests of users
over time. As a result, sequential recommender systems are proposed to model
the sequential nature of users’ interactions (Chen et al., 2018; Liu et al.,
2016; Ma et al., 2020). Besides, attention mechanism has been widely adapted
to recommender systems since its out-breaking success in NLP (Devlin et al.,
2018; Lu et al., 2019). It is leveraged between users and contents to capture
the most representative information or provide good interpretability for
recommendation (Kang and McAuley, 2018; Li et al., 2019b; Cen et al., 2020).

In real-world applications, hybrid recommendation framework is usually applied
which makes up for the shortcomings of using a single method and maximizes the
advantages. Our work is typically within the hybrid system for cross-domain
cold-start recommendation, where all strategies mentioned above are involved.

###  2.2. User Preference Learning

The core of a recommender system is to model the dynamic user preferences.
Previous works usually represent a user’s historical behavior with one single
latent vector which may suffer from correlation loss (Chen et al., 2018).
Clustering-based approaches offer an alternative to traditional model-based
methods and cluster similar users or items together (Rafailidis and Crestani,
2016; Liji et al., 2018). However, these methods rely heavily on manual
selection of a user’s attribute and profile, or treat different domains
separately. Recently, recommendations with memory network (Chen et al., 2018;
Zhou et al., 2019) are proposed to model user preference and store the long
term interest. The basic idea is to maintain a key-value style memory matrix
with numbers of slots. A user’s embedding is fed into the matrix where
similarity between the user and each key vector is computed and converted to
relevance probability using softmax function. In our work, a hierarchical
memory tree is utilized for user preference learning. Different from previous
memory-based network, our tree structure has a much larger number of memory
slots (i.e. few hundred or thousand vs. few dozens). What is more, we only
pick the top memory slots each time with calculated correlation score instead
of using all the memory slots.

###  2.3. Orthogonal Regularization

The orthogonality implies energy preservation and is proved to be efficient
for stabilizing the distribution of activations over layers with CNNs.
Orthogonal regularizers are extended to fully-connected layers and a Spectral
Restricted Isometry Property (SRIP) regularizer is proposed to guarantee
better convergence (Bansal et al., 2018). Later on, more investigations (Jia
et al., 2019; Chen et al., 2019) further extend SRIP regularization bounds and
bring compatible results on applications like image classification and Person
Re-Identification. We also apply such orthogonal regularization scheme for the
user group preference learning, which will be illustrated in detail in Section
3.

##  3\. The Proposed Method

Figure 2. Framework of our proposed method. Three levels of user preferences
are modeled, including user history, user content and user group. The whole
framework updates in a contrastive way with a Fisrt-In-First-Out (FIFO) queue,
where a large number of negative samples from latest steps is maintained for
more consistant training.

In this section, we present the problem formulation of cross-domain cold-start
recommendation first. Then we explain in detail how we model user preference
from three different aspects in COUPLE and train the framework efficiently in
a contrastive way. The overall design of our proposed COUPLE network is shown
in Figure 2.

###  3.1. Problem Formulation and Notations

####  3.1.1. Problem Formulation

Cross-domain recommendation in real-world may involve several channels (Xie et
al., 2020). Without loss of generality, we classify those channels into source
domain(s) A and target domain(s) B, where user interactions are much denser in
A compared to B. We denote $\mathcal{U}_{A}$, $\mathcal{U}_{B}$ as the sets of
users and $\mathcal{I}_{A}$, $\mathcal{I}_{B}$ as the sets of interacted items
with content features (semantic tags in our case) respectively. We also have a
cold-start item set in target domain denoted as
$\mathcal{I}_{B}^{{}^{\prime}}$ where items are with limited (or none)
interactions. For the cross-domain cold-start recommendation, we have a) user
overlap $\mathcal{U}_{A}\cap\mathcal{U}_{B}\neq\emptyset$ ; b) item overlap
$\mathcal{I}_{A}\cap\mathcal{I}_{B}=\emptyset$ ; c) cold-start item overlap
$\mathcal{I}_{B}\cap\mathcal{I}_{B}^{{}^{\prime}}=\emptyset$. We define two
tasks with regard to the training and inference processes of COUPLE,
respectively:

  * •

Joint recommendation for training, i.e., make recommendation on items in
$\mathcal{I}_{A}\cup\mathcal{I}_{B}$ to users
$\mathcal{U}_{A}\cup\mathcal{U}_{B}$.

  * •

Cold-start recommendation for inference, i.e., make recommendation on items in
$\mathcal{I}_{B}^{{}^{\prime}}$ to users $\mathcal{U}_{A}\cup\mathcal{U}_{B}$.

It is noted that our work can be easily extended to recommendation on items
with limited interactions as well. Notations are summarized in Table 1.

Table 1. Notations Used in Section 3. Notation | Description
---|---
$\mathcal{U}$, $\mathcal{I}$, $\mathcal{T}$ | user, item and tag set
$d\in\mathbb{N}$ | latent vector dimension
$n\in\mathbb{N}$ | number of tags per item
$l\in\mathbb{N}$ | max sequence length
$\boldsymbol{e}_{u}$, $\boldsymbol{e}_{i}$, $\boldsymbol{e}_{t}\in\mathbb{R}^{d\times 1}$ | user, item, tag embedding feature
$\boldsymbol{e}_{u}^{(h)},\boldsymbol{e}_{u}^{(c)},\boldsymbol{e}_{u}^{(g)}\in\mathbb{R}^{d\times 1}$ | user history, content, group preference
$\boldsymbol{s_{i,j}}\in\mathbb{R}^{d\times 1}$ | tree node vector at position $j$ in layer $i$
$\mathbf{M}$ | attention map
$\mathbf{W}$ | weight matrix
$\mathcal{L}$ | loss
$\|.\|$ | norm
[.] | concatenation

###  3.2. Cross-domain User Preference Learning

As illustrated in Figure 2, we model a user’s preference from three
interactive stages. First, user’s history preference is modeled with a domain-
aware multi-head attention scheme for sequential behaviors from different
domains. Then it will attend to the underlying tag-level features to encode
tag importance for user content preference. A hierarchical memory tree is used
to represent user’s historical preference with “orthogonal” leaf-node vectors.
Finally, user preferences from three aspects are weighted aggregated.

####  3.2.1. User History Preference

We model a user’s historical behavior using a deep sequential model, where
item-level attention scheme is applied. In standard sequential models, a
sequence of item index is often given for embedding lookup (Kang and McAuley,
2018; Ma et al., 2020). However, in cold-start content recommendation, items
may be never seen or interacted before. To solve this issue, we use the global
semantic tags to represent each item. To be more specific, we obtain a cross-
domain tag set $\mathcal{T}$ from items across domains
$\mathcal{I}_{A}\cup\mathcal{I}_{B}$. The tags can be extracted from hashtag
made by users, item attributes or genres, or from images and texts pre-
processed by vision and language models. A fair assumption can be made that
the tag set $\mathcal{T}$ is able to cover most of the items in
$\mathcal{I}_{B}^{{}^{\prime}}$ from the target domain.

Our input for each item is a group of tags $[t_{1},t_{2},\dots,t_{n}]$, where
$t_{x}\in\\{1,2,\dots,N\\}$ is the index of the tag in the whole set
$\mathcal{T}$ with size $N$. A tag embedding table
$\mathbf{H}_{t}\in\mathbb{R}^{d\times N}$ takes tag index sequence as the
input and outputs the representation of the tag features
$[\boldsymbol{e}_{t,1},\boldsymbol{e}_{t,2},\dots,\boldsymbol{e}_{t,n}]$,
where $\boldsymbol{e}_{t}\in\mathbb{R}^{d\times 1}$. In this way, we represent
an item $\boldsymbol{e}_{i}\in\mathbb{R}^{d\times 1}$ by aggregating the tag
features by average pooling:

(1)
$\boldsymbol{e}_{i}=\text{AvgPool}(\\{\boldsymbol{e}_{t}\\}_{k=1}^{n})=\frac{1}{n}\sum_{k=1}^{n}\boldsymbol{e}_{t,k},$

where $n$ is the number of tag features capped for each item. Note that the
index-based embedding lookup scheme can be easily extended to using multi-
modal embeddings from any pre-trained models. To explicitly involve the
domain-specific knowledge, we follow the design in Bert (Devlin et al., 2018)
and add a domain embedding table $\mathbf{H}_{d}\in\mathbb{R}^{d\times Q}$
($Q$ is the number of channels) to the current item feature embedding, for
training. For inference and online serving, we only use the tag features for
item embedding, as suggested by the recent recommendation work (Zhou et al.,
2020).

To model user history preference, we apply a multi-head attention (MHAttn)
mechanism (Kang and McAuley, 2018) to the sequence of temporally sorted items
$[\boldsymbol{e}_{i,1},\boldsymbol{e}_{i,2},\dots,\boldsymbol{e}_{i,l}]$
clicked (rated) by users. Self-attention is applied to aggregate all item
embeddings with adaptive weights and followed by two-layer feed-forward
networks (FFN) to increase non-linearity.

(2)
$(\boldsymbol{e}_{u,1},\dots,\boldsymbol{e}_{u,m})=\text{MHAttn}(\\{\boldsymbol{e}_{i,k}\\}_{k=1}^{l}),$

where $l$ is the max sequence length and $m$ is the number of attention heads.
Furthermore, we perform weighted aggregation (WA) to obtain user history
preference $\boldsymbol{e}_{u}^{(h)}$ on the output representations
$\\{\boldsymbol{e}_{u}\\}_{k=1}^{m}$ of Eq. (2) as:

(3)
$\boldsymbol{e}_{u}^{(h)}=\text{WA}(\\{\boldsymbol{e}_{u}\\}_{k=1}^{m})=\text{WA}([\boldsymbol{e}_{u,1},\dots,\boldsymbol{e}_{u,m}]),$

with a parameter matrix $\mathbf{M}\in\mathbb{R}^{d\times d}$ learnt and
updated, the following procedure is performed:

(4)
$\begin{split}&\boldsymbol{e}_{m}=\frac{1}{m}\sum_{k=1}^{m}\boldsymbol{e}_{u,k},\quad\boldsymbol{d}_{k}=\boldsymbol{e}_{u,k}^{T}\mathbf{M}\boldsymbol{e}_{m},\\\
&a_{k}=\frac{\exp\left(\boldsymbol{d}_{k}\right)}{\sum_{k^{\prime}=1}^{m}\exp\left(\boldsymbol{d}_{k^{\prime}}\right)},\quad\boldsymbol{e}_{u}^{(h)}=\sum_{k=1}^{m}a_{k}\boldsymbol{e}_{u,k}.\end{split}$

####  3.2.2. User Content Preference

User history feature obtained from Section 3.2.1 focuses on the item-level
attention, where each tag contributes equally for an item representation.
However, same tags appearing multiple times in the item sequence are supposed
to contribute more to a user’s interest. The similar conclusion on the
importance of item frequency for next-bucket recommendation has been made
recently in (Hu et al., 2020). As a result, we propose a frequency encoder
which emphasizes the appearances of the same tags. It is implemented by a
cross-layer attention process.

We concatenate all the tag embeddings in the item sequence together as
$\\{\boldsymbol{e}_{t}\\}_{k=1}^{n\times{l}}$=$[\boldsymbol{e}_{t,1},\boldsymbol{e}_{t,2},\dots,\boldsymbol{e}_{t,n\times{l}}]$,
and let them go through a one-layer MLP with a hyperbolic tangent function.
This results in a hidden representation $\boldsymbol{h}_{t}$. Then the softmax
function is applied between $\boldsymbol{h}_{t}$ and the user’s history
representation $\boldsymbol{e}_{u}^{(h)}$ to obtain the attention weights. The
user content representation $\boldsymbol{e}_{u}^{(c)}$ is computed as the
weighted sum of attention weights and the tag features:

(5)
$\begin{split}&\boldsymbol{h}_{t,i}=\operatorname{tanh}(\textbf{W}_{w}\boldsymbol{e}_{t,i}+b_{w}),\quad
a_{i}=\frac{\exp\left(\boldsymbol{e}_{u}^{(h)}\cdot\boldsymbol{h}_{t,i}\right)}{\sum_{i^{\prime}=1}^{n\times{l}}\exp\left(\boldsymbol{e}_{u}^{(h)}\cdot\boldsymbol{h}_{t,i^{\prime}}\right)},\\\
&\boldsymbol{e}_{u}^{(c)}=\sum_{i=1}^{n\times{l}}a_{i}\boldsymbol{e}_{t,i}.\end{split}$

In this way, the same tag with multiple attention weights will be augmented in
the final representation of user content preference. A simple illustration of
how this frequency encoder works is shown in Figure.3. From the design point
of view, the user history representation is modeled based on a bottom-up
attention while the user content preference is in a top-down fashion. Such
cross-layer attention is proved to be critical to boost interactions between
the high-level representation with the low-level content source (Anderson et
al., 2018; Lu et al., 2019).

Figure 3. Tag-level Frequency Encoder. Representation of the same tag will be
aggregated and augmented after user-tag attention scheme (best viewed in
color).

####  3.2.3. User Group Preference

Unlike previous cross-domain works where only the overlapped users are
considered, we take into account all the users’ behavior patterns and try to
find out a uniform representation for user group preference across domains.
Consequently, a hierarchical memory tree is designed to remember a user’s
general interest and automatically classify it into groups with closest
interests. It differs from the original memory networks in that : a) we are
able to have more memory slots as proved in the recent work (Shi et al., 2020)
(i.e. few hundreds or thousands vs. few dozens); and b) we don’t use all slots
as memory networks do, instead we pick the top $K$ leaf-node slots each time
with highest scores.

Tree Structure Design. With user history representation from equation (4), we
follow the similar procedure as (Shi et al., 2020) to use a hierarchically
fully-connected tree where the root node allocates weights to children nodes
and finally leaf nodes. To enforce further interpretability, the sum of the
node weights at the same layer is equal to 1 and the sum of children node
weights inherited from the same parent node is equal to the parent node
weight. Given user history representation $\boldsymbol{e}_{u}^{(h)}$ and a
parent node at position $j$ in layer $i$ with $h$ children nodes, whose weight
is denoted as ${w}_{i,j}$, the weights of the children nodes in layer $i+1$
can be calculated using softmax function:

(6)
$\begin{split}w_{i+1,k}&={w}_{i,j}\cdot\operatorname{softmax}(\boldsymbol{e}_{u}^{(h)}\cdot\boldsymbol{s}_{i+1,k})\\\
&={w}_{i,j}\cdot\frac{\exp(\boldsymbol{e}_{u}^{(h)}\cdot\boldsymbol{s}_{i+1,k})}{\sum_{l}\exp(\boldsymbol{e}_{u}^{(h)}\cdot\boldsymbol{s}_{i+1,l}))},\quad\forall
l=1,2,\cdots,h\end{split}$

where $\boldsymbol{s}_{i+1,k}$ is the memory slot vector at position $k$ of
layer $i+1$.

Dead-node Solution. During the training process of retrieving top $K$ leaf-
node vectors, we met the same problem as (Shi et al., 2020) where almost the
same set of nodes where visited at each step. The paper dealt with this
problem by uniformly choosing $K$ random candidates each time thus solving the
dead-node problem at the early stage of training. However, as the model
parameters update along time, real top-$K$ node vectors are desired to be
retrieved.

In our work, we use Gumbel-Softmax (Jang et al., 2016) which is an ideal
sampling trick for distribution on discrete vectors (also known as
reparameterization trick). The basic idea of Gumbel-Softmax is to add a Gumbel
noise and temperature factor to the original softmax function so that it is
able to approximate a probability distribution made up of discrete categories
(which are the normalized leaf-node weights in our case).

With calculated leaf-node weights (i.e. probabilities)
$w_{1},w_{2},\dots,w_{k}$ from softmax function using Eq. (6), the Gumbel-
Softmax is conducted as:

(7)
$\begin{split}y_{i}&=\operatorname{softmax}((\operatorname{log}({w_{i}})+g_{i})/\tau)\\\
&=\frac{\exp((\operatorname{log}({w_{i}})+g_{i})/\tau)}{\sum_{j}\exp((\operatorname{log}({w_{j}})+g_{j})/\tau)},\quad\forall
j=1,2,\cdots,k\end{split}$

where $g_{1},g_{2},\dots,g_{k}$ are i.i.d samples drawn from the standard
Gumbel distribution having $\mu$ and $\beta$ as 0 and 1 respectively, with PDF
(Probability Density Function) of $e^{-(x+e^{-x})}$. In practice, $g_{k}$ can
be sampled using inverse transform sampling by drawing
$u_{k}\sim\text{uniform}(0,1)$ and calculated as $g_{k}=-\log(-\log(u_{k}))$
(Maddison et al., 2016).

One of the great property of the Gumbel-Softmax is that the output value
approaches the real distribution with low temperature factor $\tau$ and tends
to be uniform sampling with larger $\tau$. As a result, we start the training
with a big temperature and then anneal it towards small values. In this way,
the model tends to explore random nodes for update in the beginning and
gradually stick to the real top $K$ selection for a better convergence.

For inference, the Top $K$ leaf-node vectors with highest weight scores are
used to form the user group representation $\boldsymbol{e}_{u}^{(g)}$:

(8)
$\boldsymbol{e}_{u}^{(g)}=\sum_{k=1}^{K}w_{k}^{(leaf)}\boldsymbol{s}_{k}^{(leaf)}.$

Orthogonality. To make the nodes at each layer more diverse and
representative, orthogonality regularizer is applied to the fully-connected
layers $\mathbf{W}$ in the tree:

(9) $\mathcal{L}_{O}=\lambda\cdot\sigma(\mathbf{W}^{T}\mathbf{W}-\mathbf{I}),$

where $\lambda$ is the penalty parameter and
$\sigma(\mathbf{W})=\sup_{x\in\mathbb{R}^{1\times n},x\neq
0}\frac{\|\mathbf{W}x\|}{\|x\|}$ is the spectral norm of $\mathbf{W}$, i.e.
the largest singular value of $\mathbf{W}$. Though computation of Eq. (9)
involves expensive eigen-decomposition, it can be approximated via power
iteration method (Bansal et al., 2018). Starting with a random initialized
vector $\boldsymbol{v}\in\mathbb{R}^{d}$, we iteratively perform the following
procedures a small number of times (2 by default):

(10)
$\boldsymbol{u}\leftarrow(\mathbf{W}^{T}\mathbf{W}-\mathbf{I})\boldsymbol{v},\boldsymbol{v}\leftarrow(\mathbf{W}^{T}\boldsymbol{W}-\mathbf{I})\boldsymbol{u},\sigma(\mathbf{W}^{T}\mathbf{W}-\mathbf{I})\leftarrow\frac{\|\boldsymbol{v}\|}{\|\boldsymbol{u}\|}.$

Our hierarchical tree-based memory module is similar to previous work (Shi et
al., 2020) in design. However, the main purpose and realization is quite
different:

  * •

The PreHash module proposed in (Shi et al., 2020) is designed to solve user
embedding problem where certain anchor vectors are manually selected and kept
unchanged during training. In our work, the memory tree is designed for user
group classification and is fully automatic with parameters updating. All the
user behavior representations will go through this module and fall into most
related leaf slots.

  * •

Orthogonality property is applied to our memory tree as it is a strong
regularization for the diverse representation and ensures better convergence
of our tree module while PreHash in (Shi et al., 2020) doesn’t have this for
model update.

  * •

Sampling strategy during training is also different. Prehash uses the uniform
sampling throughout training while the Gumbel-softmax sampling applied in
COUPLE is more efficient for node representation update.

After obtaining user history representation (in Section 3.2.1), user content
representation (in Section 3.2.2) and user group representation (in Section
3.2.3), we apply weighted aggregation (WA) again to get the final user
representation $\boldsymbol{e}_{u}$ using Eq. (3):

(11) $\boldsymbol{e}_{u}=\text{WA}([e_{u}^{(h)},e_{u}^{(c)},e_{u}^{(g)}]).$

###  3.3. Contrastive Learning

Unsupervised representation learning in a contrastive way is highly successful
in recently research (Radford et al., 2018; Devlin et al., 2018; He et al.,
2020). Following a standard contrastive definition (Hadsell et al., 2006), we
define a contrastive loss between our user representaion $\boldsymbol{e}_{u}$
and item representation
$\boldsymbol{e}_{i,0}$,$\boldsymbol{e}_{i,1}$,…,$\boldsymbol{e}_{i,m}$:

(12)
$\mathcal{L}_{N}=-\mathbb{E}[\log\frac{\exp(\boldsymbol{e}_{u}\cdot\boldsymbol{e}_{i}^{+}/\omega)}{\exp(\boldsymbol{e}_{u}\cdot\boldsymbol{e}_{i}^{+}/\omega)+\sum_{j=1}^{m-1}\exp(\boldsymbol{e}_{u}\cdot\boldsymbol{e}_{j}^{-}/\omega)}],$

where $\omega$ is a temperature hyper-parameter. The contrasitve loss has a
low value when $\boldsymbol{e}_{u}$ is similar to its positive item sample
$\boldsymbol{e}_{i}^{+}$ and dissimilar to all other negative item samples
$\\{\boldsymbol{e}_{j}^{-}\\}$.

In earlier study, softmax-based classifier is often utilized to classify
between positive and negative samples. In (He et al., 2020), an efficient
momentum contrastive scheme is proposed to maintain the dictionary as a queue
of data samples. In this way, a rich set of negative samples can be involved
for training and achieve positive results in various computer vision tasks. In
our framework, a First-In-First-Out (FIFO) quque is maintained and updated
with the current batch enqueued and the oldest batch dequeued for each
training step. So that each batch of positive samples can be encoded with the
hard negative samples over the latest steps. It makes the loss tracking more
consistent and has a debiasing effect in large-scale production environment as
proved in (Zhou et al., 2020). Thus, our network is trained under the loss
function $\mathcal{L}=\mathcal{L}_{N}+\mathcal{L}_{O}$ consisting of a
contrastive loss and a orthogonal constraint on weights of memory tree.

##  4\. Experiments

In this section, we evaluate our proposed cross-domain user preference
learning (COUPLE) model for top-$K$ retrieval task under different scenarios.
We introduce the experimental setup and the comparing baselines first, and
present the performance comparison with other state-of-the-arts. Then the
ablation study is carried out both quantitatively and qualitatively.

###  4.1. Experimental Setup

####  4.1.1. Dataset Overview

We compare the performance of our proposed framework with related methods for
cross-domain cold-start recommendation on two publicly accessible datasets.
Amazon review dataset111http://jmcauley.ucsd.edu/data/amazon/ is one of the
most widely-used public dataset (He and McAuley, 2016) for e-commerce
recommendations. We use subsets of Books as the source domain while Movies and
TV the target domain. The other dataset is called Tao-Product-Micro-Video
(TPMV), selected from the real-world online service of Taobao Recommendation.
User interactions are much denser in product domain than micro-video domain,
making the dataset suitable for cross-domain cold-start recommendation. The
detailed statistics of the two datasets are demonstrated in Table 2.

Table 2. Dataset statistics. Datasets | #Users | #Item | #Tags | #Interact
---|---|---|---|---
Amazon Book | 1,672,201 | 1,677,035 | 555,685 | 11,637,960
Amazon Movie | 1,080,338 | 154,451 | 73,430 | 2,561,003
Taobao Product | 951,069 | 2,794,416 | 85,398 | 158,758,876
Taobao m-Video | 829,930 | 969,145 | 56,291 | 47,332,179

####  4.1.2. Experimental Setup

To compose valid training and testing datasets for cross-domain cold-start
recommendation, we use ”click” as the implicit feedback for TPMV dataset and
”review rating” for Amazon dataset. For training and evaluation, clicked items
of TPMV and review ratings over 3 (ratings range from 1 to 5) of Amazon are
regarded as positive samples and temporally sorted with timestamps of a user’s
action. For testing, we use leave-one-out strategy and make the last-position
items from target domain as the ground-truth, while erasing these items from
the training pool to make sure they are totally cold-start contents. To
further make the situation tougher as the real circumstances, we randomly
select half of the testing users, and erase all the items of the target domain
(if any) from their historical sequences to make them cold-start users. For
all the models compared in this paper, the detailed numbers of training and
testing samples are listed in Table 3.

Table 3. Traing and testing splits. Datasets | #Train | #Test | #Cold-start User
---|---|---|---
Amazon | 5,797,557 | 95,884 | 67,063
TPMV | 5,333,879 | 62,230 | 34,934

####  4.1.3. Evaluation metrics

To evaluate the performance of all the methods, Hit Ratio (HR), and Normalized
Discounted cumulative gain (NDCG) are used. HR measures whether the positive
item retrieved within the top-$K$ and NDCG penalizes the score if positive
item positioned lower in the ranking list. Higher values in these metrics
indicate better recommendation performance. For each ground-truth positive
item, we pair it with 100 randomly sampled negative items from the pool where
users have no historical interactions with, following the prior work (He et
al., 2017; Huang et al., 2018). To make the comparison more reliable, 50 of
them are sampled randomly, while the other 50 items are sampled according to
the popularity (Huang et al., 2018).

Table 4. HitRate and NDCG of different methods on the two datasets, where best performance is in boldface. HP denotes hyperparameters, including $n$ the number of tags and $l$ the item length for sequential modeling.  Dataset | TPMV Data | Amazon Data
---|---|---
HP |  $n$ = 15, $l$ = 5 |  $n$ = 10, $l$ = 8
Metric | HitRate@5 | HitRate@10 | NDCG@5 | NDCG@10 | HitRate@5 | HitRate@10 | NDCG@5 | NDCG@10
DSSM (Huang et al., 2013) | 0.07764 | 0.12490 | 0.05397 | 0.06908 | 0.05119 | 0.09463 | 0.03093 | 0.04658
DeepCoNN (Zheng et al., 2017) | 0.19080 | 0.27351 | 0.13435 | 0.16062 | 0.05352 | 0.10278 | 0.03319 | 0.04800
1-9[0.8pt/2pt] Youtube (Covington et al., 2016) | 0.19705 | 0.28187 | 0.13899 | 0.16627 | 0.06777 | 0.12398 | 0.04174 | 0.05970
ICAN (Xie et al., 2020) | 0.20610 | 0.28502 | 0.14711 | 0.17248 | 0.07431 | 0.13071 | 0.04601 | 0.06405
1-9[0.8pt/2pt] SASRec (Kang and McAuley, 2018) | 0.20145 | 0.28491 | 0.14709 | 0.17154 | 0.06918 | 0.12410 | 0.04352 | 0.06109
ComiRec (Cen et al., 2020) | 0.20171 | 0.28539 | 0.14418 | 0.17110 | 0.07036 | 0.12684 | 0.04322 | 0.06127
Ours | 0.22444 | 0.30625 | 0.16433 | 0.19062 | 0.07753 | 0.13358 | 0.04920 | 0.06711
1-9[0.8pt/2pt] Improvement | \+ 8.89% | \+ 7.44% | \+ 11.71% | \+ 10.52% | \+ 4.30% | \+ 2.19% | \+ 6.93% | \+ 4.77%

###  4.2. Competitors

We compare our proposed framework with six baselines with neural deep learning
structures, including DSSMs, Youtube DNNs and the Sequential methods.

  * •

DSSMs. The original Deep Semantic Similarity Model (DSSM) (Huang et al., 2013)
serves as a strong baseline widely used in information retrieval, which can
perform semantic matching between a query and a document. DeepCoNN (Zheng et
al., 2017) further extends DSSM to two parallel convolutional neural networks.
One of them models user behaviors and the other models item properties from
the review texts. It achieves a strong performance in content recommendation.

  * •

Youtube DNNs. Youtube (Covington et al., 2016) is a classical deep-based
matching model for building user and item embeddings collaboratively. Layers
of depth on the top is proved effective to model non-linear interactions
between features. The latest work (Xie et al., 2020) solves multi-channel
cold-start issue based on Youtube DNN structure where SOTA result is achieved.

  * •

Sequential methods. SASRec (Kang and McAuley, 2018) encodes user’s behavior
based on a variant of Transformer and is used as the backbone for many
sequential models including ours. And we also compared to the latest
sequential method ComiRec (Cen et al., 2020) which further improves for
controllable multi-interest matching based on the previous MIND (Li et al.,
2019b).

For methods mentioned above, we follow their implementations with tuned
parameters for better comparison. Original DSSM (Huang et al., 2013) is
implemented by maximizing the conditional likelihood of clicked items given
only a closest query (item in our case). For DeepCoNN (Zheng et al., 2017), it
models similarity between user and item representations. We feed in a sequence
of items represented by tag features where convolution is applied. In terms of
sequential methods, we first average tag representations for an item as our
method does. Then item sequence is modeled the same way as the original
papers, where position embedding is added. To implement ICAN (Xie et al.,
2020), we adjust the ID input feature with tag embeddings to fit in the
content cold-start scenario, while keeping all other settings unchanged.

###  4.3. Performance Comparison

The overall performance of all the methods on both datasets is summarized in
Table 4. We can observe that our proposed COUPLE network, which models user
preference from different perspectives, consistently yields the best
performance in terms of HitRate@N and NDCG@N (N = 5, 10). We would like to
note that, among three different types of baselines, Youtube DNNs and
Sequential methods obtain better performance than DSSMs. It implies that
sufficient interactions between user and item features are crucial for
content-based recommendation. Within two-towel models, DeepCoNN gains apparent
improvement over original DSSM by modeling series of items for user
presentation instead of only one item. By adding channel-wise attention
between source and target domain, ICAN is able to achieve better performance
over original Youtube network. The same improvement can be found on ComiRec
over simple sequentially self-attention method SASRec, where multi interests
of users are learnt across domains.

Furthermore, we observe that the improvement of our method over the strongest
baselines is more significant on TPMV data (7.44% vs. 2.19% on HitRate@10) and
the performances of all the methods on TPMV Dataset are generally better than
those on Amazon Dataset. The reasons may be that: a) TPMV data have more
overlapped tags in target domain with source domain than Amazon (60% vs. 25%),
so that models can learn a better correlation between domains; and b) user
behaviors are more consistent on TPMV data which is collected from a range of
a few days compared to Amazon with a wider range of months (over 4 years).
Both attributes of TPMV favors our model where user-content attention and
user-group preference learning are performed to generalize and transfer the
interests across domains.

###  4.4. Ablation Study

We perform ablation study to further explore the effect of individual
components of our COUPLE model on performance. As shown in Table 5, our base
model with user history and domain embeddings achieves similar performance
with SASRec. An apparent improvement is observed by applying user group
preference and user content preference learning modules. The variant with
hierarchical memory tree outstands others and raise the HitRate@10 by a large
margin of 3.88%, further illustrating the effectiveness of the generalizing
user preference across domains. After combining all modules together to
represent the user, the performance is further improved. We also experiment
with the batch negative sampling strategy compared to the contrastive learning
using a FIFO queue. It can be seen that with a larger number of negative
samples, model is able to distinguish data with higher efficiency. With all
modules put together, our proposed model achieve a competitive performance for
the real-world cold-start recommendation on Taobao platform.

Table 5. Ablation Study on TPMV Dataset. | Metrics
---|---
Variants of Our Method | HR@10 | NDCG@10
Base (User History + Domain) | 0.28411 | 0.17042
Base + User-Content Preference | 0.28928 | 0.17531
Base + Memory Tree | 0.29554 | 0.18392
All User + Batch_neg | 0.3011 | 0.18787
All User + FIFO Queue | 0.30625 | 0.19062

###  4.5. Source-domain Data Sensitivity

One critical assumption of our work is that it helps with the cross-domain
recommendation by joint modeling user behaviors from both source and target
domains. In this section, We conduct experiments on two datasets the
sensitivity of our model against the amount of source domain data. By
manipulating the amount of training data, we gradually decrease the portion of
data from the source domain. As part of the testing cases is cold-user
recommendation where user behaviors only exist in the source domain, we
further disassemble HR@10 and NDCG@10 for different situations.

(a) Impact on HR of TPMV (b) Impact on NDCG of TPMV (c) Impact on HR of Amazon
(d) Impact on NDCG of Amazon

Figure 4. The impact of the source domain data.

Figure 4 shows the impact of source domain data on the performance. We can see
a clear drop on both HitRate and NDCG as the percentage of training data from
the source domain decreases. Recommending cold items to cold users are more
difficult as the overall performance is worse than recommending to users with
interactions in target domain already. What is more, with less data from the
source domain, the performance on cold-user recommendation decreases more than
the warm-user situations with increasing gap between two lines. An interesting
finding is that cold-user recommendation on Amazon data is more sensitive to
the varying source data than that on TPMV data. We believe that it is related
to the correlations between tags extracted from both domains. With less
overlapping tags, it becomes more difficult to match interest between domains
with progressively sparser source triggers.

###  4.6. Visualization of User Group Preference

A good orthogonal representation tree should be able to project and classify
users into distinct groups. To further verify whether orthogonal
regularization works, We visualize the user group representations with
t-distributed stochastic neighbor embedding (t-SNE) (Van der Maaten and
Hinton, 2008). First, we obtain the memory slot vector of leaf nodes
$\\{\boldsymbol{s}\\}_{k=1}^{h}$ via fully-connected projection of user
history representation $\boldsymbol{e}_{u}^{(h)}$. Then the leaf node group
$k$ with largest weight calculated using Eq. (6) is assigned to the user.
Following t-SNE, We treat the each component of $\boldsymbol{s}_{k}$ as an
individual point and keep only the two components that have the highest
confidence levels. For better illustration, we randomly sample 10 user groups
with 10,000 points within each and the result is shown in Figure 5.

It is obvious that the clustering result with orthogonal regularization has
higher similarity within a cluster and can separate different clusters better.
When node vectors approach orthogonal, they become de-correlated so that the
responses are much less redundant. By applying orthogonality constraints
together with Gumbel-Softmax sampling trick, we observe a stable convergence
and layer-wise distribution of the hierarchical memory tree.

(a) Clustering w/o orthogonality

(b) Clustering w/ orthogonality

Figure 5. t-SNE of clustering samples of the memory tree.

##  5\. Online Deployment

We conduct online experiments by deploying our work to guess-you-like
recommendation after purchase at Taobao platform, where brand new micro-videos
with extracted tags are displayed to users with related interest. This
scenario has over dozens of millions of active users and hundreds of thousands
of new micro-movies uploaded each day. For comparison, all the matching
methods share the same ranking stage, so that click-through-rate (CTR) can be
a fair metric and is used for evaluation. We compare our work with two
baselines that are already running online, one is author-based CF where new
videos created by the same author will be retrieved and the other is Youtube
DNN where tag features are fed into the network for similarity measurement.
Users assigned to the experiment group experience COUPLE recommendation, while
the other two control groups experience author-CF and Youtube DNN,
respectively. We run the A/B test in the heavy-traffic scenario for a week.
The CTR of the experiment group with COUPLE improves over the control group by
8.855%. Further compared to author-CF, COUPLE has a lower CTR rate (-5.6%) but
provides significant gain on exposure rate by 58.91%. And It illustrates that
with content-based recommendation scheme, more cold micro-videos get the
opportunity to be shown to users which contributes to the sustainable
development of recommender systems. In general COUPLE + author-CF improve CTR
over Youtube + author-CF by 3.15%. We replace Youtube DNN with COUPLE and it
is now serving online for the cross-domain cold micro-video recommendation.

##  6\. Conclusion

In this paper, we proposed a unified framework for cross-domain cold-start
recommendation in real world. It learns a user’s preference from three
different perspectives including user history, user content and user group. By
jointly modeling the user’s behaviors with extracted semantic tags across
domains, our work is able to perform reliable recommendation in a new domain
with limit user interactions. Fed into a contrastive learning scheme, COUPLE
achieve state-of-the-art results on two datasets and demonstrates superior
performance compared to other baselines running at Taobao APP. It has been
deployed in production at scale for cold micro-video recommendation. For the
future, we plan to integrate more heterogeneous content features into our
framework to further help with the cold-start recommendation. Another exciting
direction is to incorporate knowledge graph for information propagation
towards explainable recommendation.

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##  Appendix A Reproductivity Supplement

In this section, we provide details on both offline and online experiment
settings for reproductivity purpose.

###  A.1. Offline Experimental Details

####  A.1.1. Tag Extraction

The semantic tags used for representing items are extracted manually from
different multi-media resources. For Amazon dataset, we extract meaningful
short terms as tags from title, category, brand based on frequency and
semantic annotation algorithms (Zhang et al., 2008). For TPMV dataset, richer
tags can be drawn from product title, attributes, images via specialized in-
house models. The tag extraction process can be referred to Figure 6.

####  A.1.2. Parameter Settings of Our Method

We implement our model with Tensorflow version 1.12 where default
initialization recommended by Tensorflow is applied. We use dimension size 64
for all feature representations including tags, items and users.

User History Representation. To model user history representation, one block
of self-attention with hidden size 64 and heads of 4 is used. The tag numbers
per item and item sequence length are capped to (10, 8) and (15, 5) for TPMV
and Amazon datasets, respectively. Domain embedding is added to the item
embedding to distinguish whether the items are from source or target domain.

Memory Tree Implementation. For the hierarchical memory tree design, we use
1-32-512 as the structure while dropout rate is set to be 0.2, the penalty
parameter $\lambda$ for the SRIP regularization is set to be 0.1, and the
temperature factor $\tau$ used in Gumbel-Softmax anneals using the schedule
$\tau=\max(1,20{e}^{-rt})$ of the global training step $t$, where $\tau$ is
updated every 1000 steps and $r=1\mathrm{e}-5$ are the hyperparameters used in
our method.

Figure 6. Tag extraction process used in paper.

Contrastive Learning. The contrastive learning is performed with a FIFO queue
of size 10$\times$256 where 256 is the mini-batch size. The temperature
$\omega$ used in contrastive loss from Eq. (12) is 0.03. The Adam (Kingma and
Ba, 2014) optimizer for mini-batch gradient descent is used in our work and
the learning rate is set to be 0.0001. Some extracted tags and retrieved cases
of our work are visualized in Figure 8.

###  A.2. Online Experimental Details

Our online system is shown in Figure 7. The offline model trained with the
user behaviors is utilized for online recommendation system. A user’s
representation is inferred with recent interacted items (represented by tags).
On the other hand, new videos will go through a tag extractor and obtain the
embeddings through the model. Real-time matching will be performed via
calculating the similarity score between user and video embeddings (by inner
product). Videos with the highest scores are retrieved for ranking stage.

Figure 7. Online system workflow. Figure 8. Retrieval cases of our model.


Supplementary Table 40:  Mean performance of classifiers on stratified 4-fold
cross-validation, using all possible features, including demographic,
neighborhood and drugs dispensed. Measures of performance shown are:
Precision, Recall, F1 (balanced Precision and Recall), Matthew’s Correlation
Coefficient, the Area Under the Receiver Operating Characteristic Curve, and
the Area Under the Precision and Recall Curve.

###  11.3 No Drugs model

This model is similar to the “simple” model, except no drug features are used.

Patients:

132,722

DDI (positive):

15,527 (11.70%)

no DDI (negative):

117,195 (88.30%)

Features:

5

Demographic:

gender† ($g$), age ($y$), number of drugs ($\nu^{u}$), number of co-
administrations ($\Psi^{u}$).

Neighborhood:

None.

Drug:

None.

Classifier | Precision | Recall | $F_{1}$ | MCC | AUC ROC | AUC P/R
---|---|---|---|---|---|---
SVM | 0.7578 | 0.3791 | 0.5053 | 0.4971 | 0.9185 | 0.6539
LR | 0.7172 | 0.4170 | 0.5273 | 0.5044 | 0.9130 | 0.6391
Supplementary Table 41:  Mean performance of classifiers on stratified 4-fold
cross-validation, using only demographic features. Measures of performance
shown are: Precision, Recall, F1 (balanced Precision and Recall), Matthew’s
Correlation Coefficient, the Area Under the Receiver Operating Characteristic
Curve, and the Area Under the Precision and Recall Curve.

###  11.4 Precision & Recall and Receiver Operating Characteristic curves

Supplementary Figure 15:  Precision and Recall (P/R) curve and Receiver
operating characteristic (ROC) curve for individual cross-validation folds.
Model containing demographic and drug features. Black and green dotted line
shows the baseline and mean values, respectively.

###  11.5 Feature loadings

Supplementary Tables 42 and 43 shows the feature loading for both SVM and LR
classifiers on model “simple”.

feature | coef | feature | coef
---|---|---|---
d=Digoxin | 1.1677 | d=Acetaminophen | -0.1169
d=Diltiazem | 0.8718 | d=Tobramycin | -0.1185
d=Warfarin | 0.6938 | d=Hydrochlorothiazide | -0.1203
d=Haloperidol | 0.6879 | d=Norethisterone | -0.1225
d=Glyburide | 0.6681 | d=Propylthiouracil | -0.1242
d=Pyrimethamine | 0.6549 | d=Phenylephrine | -0.1309
d=Phenytoin | 0.6015 | d=Estrogens Conjugated | -0.1312
d=Biperiden | 0.5807 | d=Trimethoprim | -0.1325
d=Carbamazepine | 0.5752 | d=Sulfamethoxazole | -0.1325
d=Gliclazide | 0.4735 | d=Colchicine | -0.1333
d=Clonazepam | 0.4717 | d=Diclofenac | -0.1347
d=Methyldopa | 0.4617 | d=Ranitidine | -0.1374
d=Propranolol | 0.4487 | d=Neomycin | -0.1383
d=Lithium | 0.3887 | d=Bacitracin | -0.1383
d=Fluconazole | 0.3716 | d=Nimesulide | -0.1413
$\nu_{i}$ | 0.3169 | d=Fenoterol | -0.1446
d=Acetylsalicylic Acid | 0.3119 | d=Nystatin | -0.1508
$\Psi_{i,j}$ | 0.3080 | d=Albendazole | -0.1514
d=Diazepam | 0.3038 | d=Nitrofurantoin | -0.1514
d=Omeprazole | 0.2822 | d=Loratadine | -0.1611
d=Amitriptyline | 0.2810 | d=Metamizole | -0.1624
d=Iron (II) Sulfate | 0.2584 | d=Spironolactone | -0.1634
d=Ethinyl Estradiol | 0.2571 | d=Tramadol | -0.1643
d=Ibuprofen | 0.2170 | d=Dexchlorpheniramine maleate | -0.1664
d=Imipramine | 0.1825 | d=Enalapril | -0.1671
d=Fluoxetine | 0.1639 | d=Azithromycin | -0.1672
d=Verapamil | 0.1455 | d=Miconazole | -0.169
d=Timolol | 0.1452 | d=Scopolamine butylbromide | -0.171
d=Atenolol | 0.1432 | d=Metronidazole | -0.1747
d=Nortriptyline | 0.1159 | d=Cephalexin | -0.1767
d=Doxycycline | 0.1046 | d=Ipratropium Bromide | -0.1779
d=Nifedipine | 0.0973 | d=Hydrocortisone | -0.1812
d=Methylphenidate | 0.0638 | d=Metoclopramide | -0.1832
d=Vaseline | 0.0596 | d=Levodopa | -0.1872
$y$ | 0.0518 | d=Medroxyprogesterone Acetate | -0.1877
d=Phenobarbital | 0.0274 | d=Doxazosin | -0.1909
d=Prednisone | 0.0232 | d=Amlodipine | -0.1936
d=Estradiol | 0.0181 | d=Losartan | -0.1937
d=Atropine | 0.0000 | d=Metformin | -0.1943
d=Thiocolchicoside | 0.0000 | d=Mebendazole | -0.1945
d=Salbutamol | -0.0071 | d=Fluphenazine | -0.204
d=Dexamethasone | -0.0102 | d=Captopril | -0.2041
d=Penicillin G procaine | -0.0115 | d=Amiodarone | -0.2042
d=Simvastatin | -0.0191 | d=Bromazepam | -0.2063
d=Gentamicin | -0.0229 | d=Codeine | -0.2064
d=Epinephrine | -0.0347 | d=Valproic acid | -0.2083
d=Furosemide | -0.0395 | d=Penicillin G Benzathine | -0.2123
d=Carvedilol | -0.0544 | d=Aminophylline | -0.2133
d=Erythromycin | -0.0588 | d=Clavulanate | -0.2141
d=Chlorpromazine | -0.0605 | d=Clopidogrel | -0.2162
d=Methotrimeprazine | -0.0683 | d=Carbidopa | -0.2269
d=Morphine | -0.0759 | d=Insulin | -0.246
d=Levothyroxine | -0.0776 | d=Isosorbide Mononitrate | -0.269
d=Alendronate | -0.0820 | d=Nicotine | -0.3003
d=Amoxicillin | -0.0908 | d=Glucose | -0.305
d=Ciprofloxacin | -0.0937 | $g=M$ | -0.3193
d=Prednisolone | -0.0944 | $g=F$ | -0.3213
d=Permethrin | -0.0978 | d=Sodium chloride | -0.3474
d=Levonorgestrel | -0.0982 | d=Isosorbide Dinitrate | -0.351
d=Folic acid | -0.0983 | d=Oseltamivir | -0.3643
d=Promethazine | -0.1059 | d=Betamethasone | -0.4765
d=Maprotiline | -0.1073 | d=Spiramycin | -0.521
d=Norfloxacin | -0.1100 | d=Sulfadiazine | -0.5259
d=Allopurinol | -0.1148 | - | -
Supplementary Table 42: Feature weights for Support Vector Machine (SVM) classifier on model “simple”. feature | coef | feature | coef
---|---|---|---
d=Digoxin | 3.6826 | d=Norethisterone | -0.4217
d=Diltiazem | 2.7678 | d=Amoxicillin | -0.4283
d=Haloperidol | 2.3874 | d=Promethazine | -0.4327
d=Warfarin | 2.3423 | d=Colchicine | -0.434
d=Glyburide | 2.2139 | d=Hydrochlorothiazide | -0.4526
d=Phenytoin | 2.1363 | d=Norfloxacin | -0.4545
d=Carbamazepine | 2.1098 | d=Estrogens Conjugated | -0.4683
d=Biperiden | 1.9247 | d=Tobramycin | -0.4763
d=Clonazepam | 1.6984 | d=Propylthiouracil | -0.4767
d=Methyldopa | 1.6363 | d=Trimethoprim | -0.4888
d=Propranolol | 1.5735 | d=Sulfamethoxazole | -0.4888
d=Gliclazide | 1.5618 | d=Acetaminophen | -0.502
$\nu_{i}$ | 1.4941 | d=Spiramycin | -0.506
d=Fluconazole | 1.3668 | d=Ranitidine | -0.5178
d=Lithium | 1.3303 | d=Diclofenac | -0.5242
d=Acetylsalicylic Acid | 1.0479 | d=Betamethasone | -0.5301
d=Diazepam | 1.0178 | d=Nimesulide | -0.5316
d=Omeprazole | 1.0114 | d=Neomycin | -0.5318
d=Amitriptyline | 0.9684 | d=Bacitracin | -0.5318
d=Iron (II) Sulfate | 0.8905 | d=Nystatin | -0.5508
$\Psi_{i,j}$ | 0.7721 | d=Prednisolone | -0.5531
d=Ibuprofen | 0.7282 | d=Fenoterol | -0.5542
d=Pyrimethamine | 0.6518 | d=Spironolactone | -0.564
d=Fluoxetine | 0.6245 | d=Hydrocortisone | -0.5778
d=Imipramine | 0.6188 | d=Mebendazole | -0.5857
d=Atenolol | 0.5100 | d=Enalapril | -0.5955
d=Ethinyl Estradiol | 0.4965 | d=Albendazole | -0.5991
d=Verapamil | 0.3885 | d=Nitrofurantoin | -0.6128
d=Doxycycline | 0.3681 | d=Miconazole | -0.6173
$y$ | 0.3547 | d=Ipratropium Bromide | -0.619
d=Timolol | 0.3492 | d=Loratadine | -0.6196
d=Nortriptyline | 0.3217 | d=Metamizole | -0.6206
d=Nifedipine | 0.2797 | d=Scopolamine butylbromide | -0.6347
d=Levonorgestrel | 0.2220 | d=Tramadol | -0.6364
d=Phenobarbital | 0.1465 | d=Metronidazole | -0.6476
d=Vaseline | 0.1118 | d=Dexchlorpheniramine maleate | -0.6534
d=Estradiol | 0.0873 | d=Medroxyprogesterone Acetate | -0.6733
d=Prednisone | 0.0824 | d=Metformin | -0.6762
d=Epinephrine | 0.0357 | d=Azithromycin | -0.6796
d=Erythromycin | 0.0242 | d=Captopril | -0.6855
d=Thiocolchicoside | -0.0044 | d=Losartan | -0.6882
d=Atropine | -0.0128 | d=Amlodipine | -0.6899
d=Sulfadiazine | -0.0250 | d=Cephalexin | -0.6901
d=Penicillin G procaine | -0.0593 | d=Doxazosin | -0.6929
d=Salbutamol | -0.0845 | d=Metoclopramide | -0.7212
d=Phenylephrine | -0.0869 | d=Aminophylline | -0.7297
d=Simvastatin | -0.0914 | d=Codeine | -0.7311
d=Dexamethasone | -0.0917 | d=Clopidogrel | -0.7375
d=Gentamicin | -0.1000 | d=Amiodarone | -0.7402
d=Methylphenidate | -0.1019 | d=Clavulanate | -0.7449
d=Sodium chloride | -0.1856 | d=Valproic acid | -0.7461
d=Fluphenazine | -0.2091 | d=Carbidopa | -0.7552
d=Furosemide | -0.2152 | d=Bromazepam | -0.7571
d=Methotrimeprazine | -0.2171 | d=Levodopa | -0.7619
d=Carvedilol | -0.2223 | d=Penicillin G Benzathine | -0.8072
d=Chlorpromazine | -0.2356 | d=Insulin | -0.8443
d=Maprotiline | -0.2791 | d=Isosorbide Mononitrate | -0.9186
d=Morphine | -0.2889 | d=Nicotine | -0.9342
d=Levothyroxine | -0.2929 | d=Glucose | -0.9742
d=Folic acid | -0.3650 | $g=M$ | -1.116
d=Alendronate | -0.3683 | $g=F$ | -1.132
d=Allopurinol | -0.3954 | d=Isosorbide Dinitrate | -1.178
d=Permethrin | -0.4101 | d=Oseltamivir | -1.3
d=Ciprofloxacin | -0.4119 | - | -
Supplementary Table 43: Feature weights on Logistic Regression (LR) classifier
on model “simple”.