# Generalized Maximum Entropy for Supervised Classification

arXiv: https://arxiv.org/abs/2007.05447 · HTML: https://mlsanity.com/paper/2007.05447/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2020.

## Built on by (most cited first, 12 of 12)

- [Minimax risk classifiers with 0-1 loss](https://mlsanity.com/paper/2201.06487/) (2022)
- [Double-Weighting for Covariate Shift Adaptation](https://mlsanity.com/paper/2305.08637/) (2023)
- [Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure](https://mlsanity.com/paper/2312.12236/) (2023)
- [MRCpy: A Library for Minimax Risk Classifiers](https://mlsanity.com/paper/2108.01952/) (2021)
- [Minimax Classification under Concept Drift with Multidimensional Adaptation and Performance Guarantees](https://mlsanity.com/paper/2205.15942/) (2022)
- [Efficient Learning of Minimax Risk Classifiers in High Dimensions](https://mlsanity.com/paper/2306.06649/) (2023)
- [Minimax Forward and Backward Learning of Evolving Tasks with Performance Guarantees](https://mlsanity.com/paper/2310.15974/) (2023)
- [Convergence Behavior of an Adversarial Weak Supervision Method](https://mlsanity.com/paper/2405.16013/) (2024)
- [Efficient distributional regression trees learning algorithms for calibrated non-parametric probabilistic forecasts](https://mlsanity.com/paper/2502.05157/) (2025)
- [Reliable Programmatic Weak Supervision with Confidence Intervals for Label Probabilities](https://mlsanity.com/paper/2508.03896/) (2025)
- [Efficient Large-Scale Learning of Minimax Risk Classifiers](https://mlsanity.com/paper/2511.17626/) (2025)
- [Minimax Generalized Cross-Entropy](https://mlsanity.com/paper/2603.19874/) (2026)

## Abstract (arXiv)

The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision problems where it corresponds to minimax approaches. This paper establishes a framework for supervised classification based on the generalized maximum entropy principle that leads to minimax risk classifiers (MRCs). We develop learning techniques that determine MRCs for general entropy functions and provide performance guarantees by means of convex optimization. In addition, we describe the relationship of the presented techniques with existing classification methods, and quantify MRCs performance in comparison with the proposed bounds and conventional methods.