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Communication Dans Un Congrès Année : 2022

Generalized Sliced Probability Metrics

Résumé

Sliced probability metrics have become increasingly popular in machine learning, and they play a quintessential role in various applications, including statistical hypothesis testing and generative modeling. However, in a practical setting, the convergence behavior of the algorithms built upon these distances have not been well established, except for a few specific cases. In this paper, we introduce a new family of sliced probability metrics, namely Generalized Sliced Probability Metrics (GSPMs), based on the idea of slicing high-dimensional distributions into a set of their one-dimensional marginals. We show that GSPMs are true metrics, and they are related to the Maximum Mean Discrepancy (MMD). Exploiting this relationship, we consider GSPM-based gradient flows and show that, under mild assumptions, the gradient flow converges to the global optimum. Finally, we demonstrate that various choices of GSPMs lead to new positive definite kernels that could be used in the MMD formulation while providing a unique integral geometric interpretation. We illustrate the application of GSPMs in gradient flows.
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Dates et versions

hal-03935833 , version 1 (12-01-2023)

Identifiants

Citer

Soheil Kolouri, Kimia Nadjahi, Shahin Shahrampour, Umut Simsekli. Generalized Sliced Probability Metrics. ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing, May 2022, Singapore, Singapore. pp.4513-4517, ⟨10.1109/ICASSP43922.2022.9746016⟩. ⟨hal-03935833⟩
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