the features have a non-zero weight and are actually used by the prediction model. Since the L1-norm is non-differentiable, we use OWL-QN [@Andrew2007] to optimize the model.

![Conceptual overview of Supervised Event Abstraction.[]{data-label="fig:overview"}](overview_method){width="50.00000%"}

From a XES Log to a Feature Space
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### Concept extension

The low-level labels of the preceding events in a trace can contain useful contextual information for high-level label classification. Based on the n-gram of $n$ last-seen events in a trace, we can calculate the probability that the current event has a label $l$. A multinoulli distribution is estimated for each n-gram of $n$ consecutive events, based on the training data. The Conditional Random Field model requires feature functions with numerical range. A concept extension based feature function with two parameters, $n$ and $l$, is valued with the multinoulli-estimated probability of the current event having high-level label $l$ given the n-gram of the last $n$ low-level event labels.

### Organizational extension

Similar to the concept extension feature functions, multinoulli distributions can be estimated on the training set for n-grams of *resource*, *role*, or *group* attributes of the last $n$ events. Likewise, an organizational extension based feature function with three parameters, n-gram size $n$, $o\in\{resource,role,group\}$, and label 