Fenchel-Young losses

This package implements loss functions useful for probabilistic classification. More specifically, it provides

• drop-in replacements for PyTorch loss functions

• drop-in replacements for TensorFlow loss functions

• scikit-learn compatible classifiers

The package is based on the Fenchel-Young loss framework [1,2,3].

Notice from the center plot that sparsemax and Tsallis are able to produce exactly zero (sparse) probabilities unlike the logistic (softmax) loss.

Supported Fenchel-Young losses

• Multinomial logistic loss

• One-vs-all logistic loss

• Sparsemax loss (sparse probabilities!)

• Tsallis losses (sparse probabilities!)

Sparse means that some classes have exactly zero probability, i.e., these classes are irrelevant.

Tsallis losses are a family of losses parametrized by a positive real value α. They recover the multinomial logistic loss with α=1 and the sparsemax loss with α=2. Values of α between 1 and 2 enable to interpolate between the two losses.

In all losses above, the ground-truth can either be a n_samples 1d-array of label integers (each label should be between 0 and n_classes-1) or a n_samples x n_classes 2d-array of label proportions (each row should sum to 1).

Examples

scikit-learn compatible classifier:

import numpy as npfrom sklearn.datasets import make_classificationfrom fyl_sklearn import FYClassifier

X, y = make_classification(n_samples=10, n_features=5, n_informative=3,                           n_classes=3, random_state=0)
clf = FYClassifier(loss="sparsemax")
clf.fit(X, y)print(clf.predict_proba(X[:3]))

Drop-in replacement for PyTorch losses:

import torchfrom fyl_pytorch import SparsemaxLoss# integers between 0 and n_classes-1, shape = n_samplesy_true = torch.tensor([0, 2])# model scores, shapes = n_samples x n_classestheta = torch.tensor([[-2.5, 1.2, 0.5],
                      [2.2, 0.8, -1.5]])
loss = SparsemaxLoss()# loss value (caution: reversed convention compared to numpy and tensorflow)print(loss(theta, y_true))# predictions (probabilities) are stored for convenienceprint(loss.y_pred)# can also recompute them from thetaprint(loss.predict(theta))# label proportions are also allowedy_true = torch.tensor([[0.8, 0.2, 0],
                       [0.1, 0.2, 0.7]])print(loss(theta, y_true))

Drop-in replacement for tensorflow losses:

import tensorflow as tffrom fyl_tensorflow import sparsemax_loss, sparsemax_predict# integers between 0 and n_classes-1, shape = n_samplesy_true = tf.constant([0, 2])# model scores, shapes = n_samples x n_classestheta = tf.constant([[-2.5, 1.2, 0.5],
                     [2.2, 0.8, -1.5]])# loss valueprint(sparsemax_loss(y_true, theta))# predictions (probabilities)print(sparsemax_predict(theta))# label proportions are also allowedy_true = tf.constant([[0.8, 0.2, 0],
                      [0.1, 0.2, 0.7]])print(sparsemax_loss(y_true, theta))

Installation

Simply copy relevant files to your project.

References

Author

• Mathieu Blondel, 2018