Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Gachon, Erell, Cazelles, Elsa, Bigot, Jérémie
Institutions: Centre National de la Recherche Scientifique, Université de Bordeaux, Institut de Mathématiques de Bordeaux, Université Toulouse III - Paul Sabatier, Université Fédérale de Toulouse Midi-Pyrénées, Université Toulouse-I-Capitole, Institut de Recherche en Informatique de Toulouse, Université Toulouse - Jean Jaurès, Institut Polytechnique de Bordeaux, Université de Toulouse
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407310041