NeurIPS 2018oral77 citations

Nearly tight sample complexity bounds for learning mixtures of Gaussians via sample compression schemes

Hassan Ashtiani, Shai Ben-David, Nicholas Harvey, Christopher Liaw, Abbas Mehrabian, Yaniv Plan

Abstract

We prove that ϴ(k d^2 / ε^2) samples are necessary and sufficient for learning a mixture of k Gaussians in R^d, up to error ε in total variation distance. This improves both the known upper bounds and lower bounds for this problem. For mixtures of axis-aligned Gaussians, we show that O(k d / ε^2) samples suffice, matching a known lower bound.

BibTeX
@inproceedings{NEURIPS2018_70ece1e1,
 author = {Ashtiani, Hassan and Ben-David, Shai and Harvey, Nicholas and Liaw, Christopher and Mehrabian, Abbas and Plan, Yaniv},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Nearly tight sample complexity bounds for learning mixtures of Gaussians via sample compression schemes},
 url = {https://proceedings.neurips.cc/paper_files/paper/2018/file/70ece1e1e0931919438fcfc6bd5f199c-Paper.pdf},
 volume = {31},
 year = {2018}
}
Nearly tight sample complexity bounds for learning mixtures of Gaussians via sample compression schemes · NeurIPS 2018