Summary of Multivariate Stochastic Dominance Via Optimal Transport and Applications to Models Benchmarking, by Gabriel Rioux and Apoorva Nitsure and Mattia Rigotti and Kristjan Greenewald and Youssef Mroueh
Multivariate Stochastic Dominance via Optimal Transport and Applications to Models Benchmarking
by Gabriel Rioux, Apoorva Nitsure, Mattia Rigotti, Kristjan Greenewald, Youssef Mroueh
First submitted to arxiv on: 10 Jun 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper introduces a novel approach to modeling agents’ preferences in complex, multi-outcome scenarios. Building on existing work in univariate stochastic dominance, researchers have largely neglected the multivariate case, where an agent must decide between diverse outcomes. The authors leverage a characterization of multivariate first stochastic dominance through couplings, developing a statistic that assesses almost stochastic dominance under the framework of Optimal Transport with a smooth cost. They also introduce an entropic regularization and establish a central limit theorem (CLT) for the empirical statistic. This enables the development of a hypothesis testing framework and an efficient implementation using the Sinkhorn algorithm. The paper demonstrates its method in comparing Large Language Models evaluated on multiple metrics, capturing dependencies between metrics to inform statistically significant decisions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In this study, scientists are trying to help people make better choices when they have many options. They’re working on a new way to understand how people think about different possibilities and how those possibilities might turn out. The problem is that most studies only looked at one option at a time, but real-life decisions often involve multiple choices. The researchers found a way to use mathematical tools called couplings to understand how people think about many options together. They also developed a new statistic that can help us see if one choice is better than another when there are many factors involved. This could be useful in areas like language processing, where machines need to make decisions based on multiple inputs. |
Keywords
» Artificial intelligence » Regularization
