Scalable Learning from Probability Measures with Mean Measure Quantization

ArXi:2502.04907v4 Announce Type: replace-cross 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. We study a quantization-based approach in which all input measures are approximated by $K$-point discrete measures sharing a common. We establish consistency of the resulting quantized measures.