# Finding population classifiers using Frank Wolfe-based method (`xcolumns.frank_wolfe`)

`xcolumns.frank_wolfe` module implements the methods for finding the optimal population classifier using the Frank-Wolfe algorithm.
The method was first introduced and described in the paper:
> [Erik Schultheis, Wojciech Kotłowski, Marek Wydmuch, Rohit Babbar, Strom Borman, Krzysztof Dembczyński. Consistent algorithms for multi-label classification with macro-at-k metrics. ICLR 2024.](https://arxiv.org/abs/2401.16594)

The main function of the module is {func}`find_classifier_using_fw() <xcolumns.frank_wolfe.find_classifier_using_fw>`:

```{eval-rst}
.. autofunction:: xcolumns.frank_wolfe.find_classifier_using_fw
```


The function returns the {class}`RandomizedWeightedClassifier <xcolumns.frank_wolfe.RandomizedWeightedClassifier>` object that can be used for prediction.
The {class}`RandomizedWeightedClassifier <xcolumns.frank_wolfe.RandomizedWeightedClassifier>`
is a set of weighted classifiers with paramters `a` (slopes) and `b` (intercepts) for each label similiar to the form used in {func}`xcolumns.weighted_prediction.predict_weighted_per_instance`.
The module also provides the function {func}`predict_using_randomized_weighted_classifier() <xcolumns.frank_wolfe.predict_using_randomized_weighted_classifier>`
for predicting the labels using the RandomizedWeightedClassifier object.


```{eval-rst}
.. autoclass:: xcolumns.frank_wolfe.RandomizedWeightedClassifier
```

```{eval-rst}
.. autofunction:: xcolumns.frank_wolfe.predict_using_randomized_weighted_classifier
```


## Wrapper functions for specific metrics

The module provides the wrapper functions for specific metrics that can be used as arguments for the {func}`find_classifier_using_fw() <xcolumns.frank_wolfe.find_classifier_using_fw>` function as well as factory function for creating such wrapper functions.

```{eval-rst}
.. automodule:: xcolumns.frank_wolfe
   :members:
   :exclude-members: find_classifier_using_fw, RandomizedWeightedClassifier, predict_using_randomized_weighted_classifier
   :undoc-members:
   :show-inheritance:
```