Latent Space Geometric Statistics

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

Deep generative models, e.g., variational autoencoders and generative adversarial networks, result in latent representation of observed data. The low dimensionality of the latent space provides an ideal setting for analysing high-dimensional data that would otherwise often be infeasible to handle statistically. The linear Euclidean geometry of the high-dimensional data space pulls back to a nonlinear Riemannian geometry on latent space where classical linear statistical techniques are no longer applicable. We show how analysis of data in their latent space representation can be performed using techniques from the field of geometric statistics. Geometric statistics provide generalisations of Euclidean statistical notions including means, principal component analysis, and maximum likelihood estimation of parametric distributions. Introduction to estimation procedures on latent space are considered, and the computational complexity of using geometric algorithms with high-dimensional data addressed by training a separate neural network to approximate the Riemannian metric and cometric tensor capturing the shape of the learned data manifold.

TitelPattern Recognition. ICPR International Workshops and Challenges, 2021, Proceedings
RedaktørerAlberto Del Bimbo, Rita Cucchiara, Stan Sclaroff, Giovanni Maria Farinella, Tao Mei, Marco Bertini, Hugo Jair Escalante, Roberto Vezzani
Antal sider16
ISBN (Trykt)9783030687793
StatusUdgivet - 2021
Begivenhed25th International Conference on Pattern Recognition Workshops, ICPR 2020 - Virtual, Online
Varighed: 10 jan. 202115 jan. 2021


Konference25th International Conference on Pattern Recognition Workshops, ICPR 2020
ByVirtual, Online
NavnLecture Notes in Computer Science

Bibliografisk note

Funding Information:
Acknowledgment. The work presented in this paper was supported by the CSGB Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum foundation, the Villum Foundation grant 00022924, the Novo Nordisk Foundation grant NNF18OC0052000, and the NSF DMS grant number 1912030.

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

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