Upper Entropy for 2-Monotone Lower Probabilities

TL;DR

This paper investigates the computational aspects of upper entropy in credal uncertainty models, providing efficient algorithms and complexity analysis for 2-monotone lower probabilities, which are crucial for uncertainty quantification tasks.

Contribution

It offers the first strongly polynomial algorithm for computing upper entropy in 2-monotone lower probabilities and improves upon existing algorithms for these models.

Findings

The problem has a strongly polynomial solution.

Proposed algorithms significantly outperform previous methods.

Enhanced understanding of computational complexity for upper entropy in credal models.

Abstract

Uncertainty quantification is a key aspect in many tasks such as model selection/regularization, or quantifying prediction uncertainties to perform active learning or OOD detection. Within credal approaches that consider modeling uncertainty as probability sets, upper entropy plays a central role as an uncertainty measure. This paper is devoted to the computational aspect of upper entropies, providing an exhaustive algorithmic and complexity analysis of the problem. In particular, we show that the problem has a strongly polynomial solution, and propose many significant improvements over past algorithms proposed for 2-monotone lower probabilities and their specific cases.