2019-06-25-brunel19a.md

abstract	section	title	layout	series	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	publisher	container-title	volume	genre	issued	pdf	extras
We study the pointwise maximum likelihood estimation rates for a class of Gaussian mixtures that are invariant under the action of some isometry group. This model is also known as multi-reference alignment, where random rotations of a given vector are observed, up to Gaussian noise. We completely characterize the speed of the maximum likelihood estimator, by giving a comprehensive description of the likelihood geometry of the model. We show that the unknown parameter can always be decomposed into two components, one of which can be estimated at the fast rate $n^{-1/2}$, the other one being estimated at the slower rate $n^{-1/4}$. We provide an algebraic description and a geometric interpretation of these facts.	contributed	Learning rates for Gaussian mixtures under group action	inproceedings	Proceedings of Machine Learning Research	brunel19a	0	Learning rates for Gaussian mixtures under group action	471	491	471-491	471	false	Brunel, Victor-Emmanuel	given family Victor-Emmanuel Brunel	2019-06-25		PMLR	Proceedings of the Thirty-Second Conference on Learning Theory	99	inproceedings	date-parts 2019 6 25	http://proceedings.mlr.press/v99/brunel19a/brunel19a.pdf