Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension

Marina Gomtsyan, Nikita Mokrov, Maxim Panov, Yury Yanovich
Proceedings of The Eleventh Asian Conference on Machine Learning, PMLR 101:1126-1141, 2019.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v101-gomtsyan19a, title = {Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension}, author = {Gomtsyan, Marina and Mokrov, Nikita and Panov, Maxim and Yanovich, Yury}, booktitle = {Proceedings of The Eleventh Asian Conference on Machine Learning}, pages = {1126--1141}, year = {2019}, editor = {Lee, Wee Sun and Suzuki, Taiji}, volume = {101}, series = {Proceedings of Machine Learning Research}, month = {17--19 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v101/gomtsyan19a/gomtsyan19a.pdf}, url = {https://proceedings.mlr.press/v101/gomtsyan19a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension %A Marina Gomtsyan %A Nikita Mokrov %A Maxim Panov %A Yury Yanovich %B Proceedings of The Eleventh Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Wee Sun Lee %E Taiji Suzuki %F pmlr-v101-gomtsyan19a %I PMLR %P 1126--1141 %U https://proceedings.mlr.press/v101/gomtsyan19a.html %V 101 %X 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.
APA
Gomtsyan, M., Mokrov, N., Panov, M. & Yanovich, Y.. (2019). Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension. Proceedings of The Eleventh Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 101:1126-1141 Available from https://proceedings.mlr.press/v101/gomtsyan19a.html.

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