New paper details structured approximations for probability measures in Wasserstein-p distance

This paper explores how to approximate probability measures using structured methods, particularly within the Wasserstein-p distance. The research focuses on applications in machine learning, imaging, and sensor-constrained measurements. Key findings include a linear rate transfer for approximation schemes in L_p(Omega) to measures in W_p(Omega) for densities bounded away from zero, leveraging Bogovskii's theorem and the Benamou-Brenier formulation of optimal transport. The paper also presents deterministic bounds for discrete approximations, showing that compactly supported measures can achieve an optimal quantizer rate of O(N^{-1/d}) for their Wasserstein-p distance approximation. AI

IMPACT This research advances theoretical understanding of measure approximation, potentially improving algorithms in machine learning and data analysis.

RANK_REASON The cluster contains a single academic paper detailing theoretical research in machine learning and statistics. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

• arXiv
• Benamou--Brenier
• Bogovskii
• Keaton Hamm
• Lp("Omega")
• Omega
• Voronoi partitions
• Wasserstein-p distance

• paper
• other

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