Bibliographic Information: Michele Caprio. (2024). Optimal Transport for ǫ-Contaminated Credal Sets. arXiv:2410.03267v1
Research Objective: This paper aims to redefine Monge's and Kantorovich's optimal transport problems within the framework of lower probabilities, focusing on their application to ε-contaminated credal sets.
Methodology: The paper leverages the concepts of lower probabilities, pushforward lower probabilities, Choquet integrals, and ε-contaminated credal sets to reformulate the classical OT problems. It then proves the equivalence between these reformulations and the classical problems under specific conditions.
Key Findings:
Main Conclusions: This work lays the groundwork for utilizing optimal transport in the context of imprecise probabilities, particularly for robust machine learning scenarios involving ε-contaminated data. The findings suggest potential applications in areas like uncertainty quantification, robust hypothesis testing, and credal ergodic theory.
Significance: This research bridges the gap between optimal transport and imprecise probabilities, opening new avenues for handling uncertainty in machine learning. It provides a theoretically grounded framework for dealing with ambiguity in data, which is crucial for real-world applications where noise and uncertainty are prevalent.
Limitations and Future Research: The paper primarily focuses on ε-contaminated credal sets. Future research could explore the extension of these findings to other types of credal sets and investigate alternative conditioning mechanisms within the framework of lower probabilities. Further exploration of applications in specific machine learning domains, such as out-of-distribution detection, is also warranted.
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by Michele Capr... at arxiv.org 10-07-2024
https://arxiv.org/pdf/2410.03267.pdfDeeper Inquiries