# Lower-Bounded Proper Losses for Weakly Supervised Classification

arXiv: https://arxiv.org/abs/2103.02893 · HTML: https://mlsanity.com/paper/2103.02893/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 4 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Adversarial Logit Pairing](https://mlsanity.com/paper/1803.06373/) (2018)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning with Fenchel-Young Losses](https://mlsanity.com/paper/1901.02324/) (2019)
- [Learning with Biased Complementary Labels](https://mlsanity.com/paper/1711.09535/) (2017)
- [Learning from Complementary Labels](https://mlsanity.com/paper/1705.07541/) (2017)
- [Robust Bi-Tempered Logistic Loss Based on Bregman Divergences](https://mlsanity.com/paper/1906.03361/) (2019)
- [Complementary-Label Learning for Arbitrary Losses and Models](https://mlsanity.com/paper/1810.04327/) (2018)
- [Structured Prediction with Partial Labelling through the Infimum Loss](https://mlsanity.com/paper/2003.00920/) (2020)
- [Mitigating Overfitting in Supervised Classification from Two Unlabeled Datasets: A Consistent Risk Correction Approach](https://mlsanity.com/paper/1910.08974/) (2019)
- [Unbiased Risk Estimators Can Mislead: A Case Study of Learning with Complementary Labels](https://mlsanity.com/paper/2007.02235/) (2020)
- [A General Theory for Structured Prediction with Smooth Convex Surrogates](https://mlsanity.com/paper/1902.01958/) (2019)
- [Generalized Mixability via Entropic Duality](https://mlsanity.com/paper/1406.6130/) (2014)
- [Learning from Indirect Observations](https://mlsanity.com/paper/1910.04394/) (2019)

## Built on by (most cited first, 1 of 1)

- [EAA-Net: Rethinking the Autoencoder Architecture with Intra-class Features for Medical Image Segmentation](https://mlsanity.com/paper/2208.09197/) (2022)

## Abstract (arXiv)

This paper discusses the problem of weakly supervised classification, in which instances are given weak labels that are produced by some label-corruption process. The goal is to derive conditions under which loss functions for weak-label learning are proper and lower-bounded -- two essential requirements for the losses used in class-probability estimation. To this end, we derive a representation theorem for proper losses in supervised learning, which dualizes the Savage representation. We use this theorem to characterize proper weak-label losses and find a condition for them to be lower-bounded. From these theoretical findings, we derive a novel regularization scheme called generalized logit squeezing, which makes any proper weak-label loss bounded from below, without losing properness. Furthermore, we experimentally demonstrate the effectiveness of our proposed approach, as compared to improper or unbounded losses. The results highlight the importance of properness and lower-boundedness.