Statistical Learning Guarantees for Compressive Clustering and Compressive Mixture Modeling
Abstract
We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The principle of compressive statistical learning is to compress a training collection, in one pass, into a low-dimensional sketch (a vector of random empirical generalized moments) that captures the information relevant to the considered learning task. We explicitly describe and analyze random feature functions which empirical averages preserve the needed information for compressive clustering and compressive Gaussian mixture modeling with fixed known variance, and establish sufficient sketch sizes given the problem dimensions.
Cite
@article{arxiv.2004.08085,
title = {Statistical Learning Guarantees for Compressive Clustering and Compressive Mixture Modeling},
author = {Rémi Gribonval and Gilles Blanchard and Nicolas Keriven and Yann Traonmilin},
journal= {arXiv preprint arXiv:2004.08085},
year = {2021}
}
Comments
This preprint results from a split and profound restructuring and improvements of of https://hal.inria.fr/hal-01544609v2It is a companion paper to https://hal.inria.fr/hal-01544609v3. Mathematical Statistics and Learning, EMS Publishing House, In press