Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2025

Scalable Learning from Probability Measures with Mean Measure Quantization

Résumé

We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the measures have large support. We study a quantization-based approach in which all input measures are approximated by $K$-point discrete measures sharing a common support. We establish consistency of the resulting quantized measures. We further derive convergence guarantees for several OT-based downstream tasks computed from the quantized measures. Numerical experiments on synthetic and real datasets demonstrate that the proposed approach achieves performance comparable to individual quantization while substantially reducing runtime.

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Dates et versions

hal-04941078 , version 1 (11-02-2025)
hal-04941078 , version 2 (24-03-2026)

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Erell Gachon, Elsa Cazelles, Jérémie Bigot. Scalable Learning from Probability Measures with Mean Measure Quantization. 2026. ⟨hal-04941078v2⟩
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