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).
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))
The TensorFlow implementation requires the installation of TensorFlow-addons (<https://github.com/tensorflow/addons>) Simply copy relevant files to your project.
|||SparseMAP: Differentiable Sparse Structured Inference. Vlad Niculae, André F. T. Martins, Mathieu Blondel, Claire Cardie. In Proc. of ICML 2018. [arXiv]|
|||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]|
|||Learning with Fenchel-Young Losses. Mathieu Blondel, André F. T. Martins, Vlad Niculae. Preprint. [arXiv]|
- Mathieu Blondel, 2018