Academic

Upper Entropy for 2-Monotone Lower Probabilities

arXiv:2603.23558v1 Announce Type: new 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.

T
Tuan-Anh Vu, S\'ebastien Destercke, Fr\'ed\'eric Pichon · · 1 min read · 9 views
#cs.LG #cs.AI

arXiv:2603.23558v1 Announce Type: new 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.

Executive Summary

This article presents an exhaustive algorithmic and complexity analysis of upper entropies for 2-monotone lower probabilities, a crucial aspect in uncertainty quantification. The authors develop a strongly polynomial solution and propose significant improvements over existing algorithms. The study has far-reaching implications for model selection, regularization, active learning, and out-of-distribution (OOD) detection. This research contributes to the advancement of credal approaches in uncertainty modeling, which is essential in decision-making under uncertainty. The proposed solution offers a scalable and efficient tool for practitioners and researchers, enabling reliable uncertainty quantification and improved decision-making. The article provides valuable insights into the computational aspects of upper entropies, shedding light on the underlying complexities and potential applications.

Key Points

  • ▸ The authors develop a strongly polynomial solution for upper entropies of 2-monotone lower probabilities.
  • ▸ Significant improvements are proposed over existing algorithms for 2-monotone lower probabilities and their specific cases.
  • ▸ The study has implications for model selection, regularization, active learning, and OOD detection.
  • ▸ The research advances credal approaches in uncertainty modeling and offers a scalable and efficient tool for practitioners.

Merits

Strength in Algorithmic Development

The authors' work demonstrates a comprehensive understanding of the computational aspects of upper entropies, leading to the development of a strongly polynomial solution and significant algorithmic improvements.

Contribution to Credal Approaches

This research advances the field of credal approaches in uncertainty modeling, providing a reliable and efficient tool for uncertainty quantification and decision-making under uncertainty.

Demerits

Limited Generalizability

The study focuses on 2-monotone lower probabilities, which may limit the generalizability of the proposed solution to other types of uncertainty models.

Computational Complexity

While the proposed solution is polynomial, the computational complexity may still be high for large-scale applications, requiring further optimization and refinement.

Expert Commentary

This article presents a significant contribution to the field of uncertainty modeling, particularly in credal approaches. The authors' work demonstrates a comprehensive understanding of the computational aspects of upper entropies and provides a reliable and efficient tool for uncertainty quantification. The proposed solution has far-reaching implications for model selection, regularization, active learning, and OOD detection. While the study focuses on 2-monotone lower probabilities, the insights gained can be applied to other types of uncertainty models, advancing the field of uncertainty modeling and enabling more informed decision-making under uncertainty.

Recommendations

  • ✓ Future research should focus on generalizing the proposed solution to other types of uncertainty models.
  • ✓ The authors should investigate further optimization and refinement of the computational complexity for large-scale applications.

Sources

Original: arXiv - cs.LG

Related Articles