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 np
from sklearn.datasets import make_classification
from 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 torch
from fyl_pytorch import SparsemaxLoss

# integers between 0 and n_classes-1, shape = n_samples
y_true = torch.tensor([0, 2])
# model scores, shapes = n_samples x n_classes
theta = 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 convenience
print(loss.y_pred)
# can also recompute them from theta
print(loss.predict(theta))
# label proportions are also allowed
y_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 tf
from fyl_tensorflow import sparsemax_loss, sparsemax_predict

# integers between 0 and n_classes-1, shape = n_samples
y_true = tf.constant([0, 2])
# model scores, shapes = n_samples x n_classes
theta = tf.constant([[-2.5, 1.2, 0.5],
                     [2.2, 0.8, -1.5]])
# loss value
print(sparsemax_loss(y_true, theta))
# predictions (probabilities)
print(sparsemax_predict(theta))
# label proportions are also allowed
y_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.

The TensorFlow implementation requires the installation of TensorFlow Addons.

References

[1]	SparseMAP: Differentiable Sparse Structured Inference. Vlad Niculae, André F. T. Martins, Mathieu Blondel, Claire Cardie. In Proc. of ICML 2018. [arXiv]

[2]	Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms. Mathieu Blondel, André F. T. Martins, Vlad Niculae. In Proc. of AISTATS 2019. [arXiv]

[3]	Learning with Fenchel-Young Losses. Mathieu Blondel, André F. T. Martins, Vlad Niculae. Preprint. [arXiv]

Author

• Mathieu Blondel, 2018