2019-10-15-gomtsyan19a.md

title	crossref	abstract	layout	series	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	publisher	container-title	volume	genre	issued	pdf	extras
Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension	acml19	The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown support leads to the polynomial correction to the standard maximum likelihood estimate of intrinsic dimension for flat manifolds. The proposed algorithm (GeoMLE) realizes the correction by regression of standard MLEs based on distances to nearest neighbors for different sizes of neighborhoods. Moreover, the proposed approach also efficiently handles the case of nonuniform sampling of the manifold. We perform a series of experiments on various synthetic and real-world datasets. The results show that our algorithm achieves state-of-the-art performance, while also being robust to noise in the data and competitive computationally.	inproceedings	Proceedings of Machine Learning Research	gomtsyan19a	0	Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension	1126	1141	1126-1141	1126	false	Gomtsyan, Marina and Mokrov, Nikita and Panov, Maxim and Yanovich, Yury	given family Marina Gomtsyan given family Nikita Mokrov given family Maxim Panov given family Yury Yanovich	2019-10-15		PMLR	Proceedings of The Eleventh Asian Conference on Machine Learning	101	inproceedings	date-parts 2019 10 15	http://proceedings.mlr.press/v101/gomtsyan19a/gomtsyan19a.pdf