Sliced Wasserstein with Random-Path Projecting Directions Article Swipe

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Minh‐Khai Nguyen , Shujian Zhang , Tam Le , Nhat Ho ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2401.15889

Slicing distribution selection has been used as an effective technique to improve the performance of parameter estimators based on minimizing sliced Wasserstein distance in applications. Previous works either utilize expensive optimization to select the slicing distribution or use slicing distributions that require expensive sampling methods. In this work, we propose an optimization-free slicing distribution that provides a fast sampling for the Monte Carlo estimation of expectation. In particular, we introduce the random-path projecting direction (RPD) which is constructed by leveraging the normalized difference between two random vectors following the two input measures. From the RPD, we derive the random-path slicing distribution (RPSD) and two variants of sliced Wasserstein, i.e., the Random-Path Projection Sliced Wasserstein (RPSW) and the Importance Weighted Random-Path Projection Sliced Wasserstein (IWRPSW). We then discuss the topological, statistical, and computational properties of RPSW and IWRPSW. Finally, we showcase the favorable performance of RPSW and IWRPSW in gradient flow and the training of denoising diffusion generative models on images.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2401.15889
PDF: https://arxiv.org/pdf/2401.15889
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4391376518

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DOI: https://doi.org/10.48550/arxiv.2401.15889

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Title: Sliced Wasserstein with Random-Path Projecting Directions

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-01-29

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Authors: Minh‐Khai Nguyen, Shujian Zhang, Tam Le, Nhat Ho

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Landing page: https://arxiv.org/abs/2401.15889

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PDF URL: https://arxiv.org/pdf/2401.15889

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Concepts: Path (computing), Mathematics, Computer science, Computer network

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