Latent Space Geometric Statistics
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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Latent Space Geometric Statistics. / Kühnel, Line; Fletcher, Tom; Joshi, Sarang; Sommer, Stefan.
Pattern Recognition. ICPR International Workshops and Challenges, 2021, Proceedings. red. / Alberto Del Bimbo; Rita Cucchiara; Stan Sclaroff; Giovanni Maria Farinella; Tao Mei; Marco Bertini; Hugo Jair Escalante; Roberto Vezzani. Springer, 2021. s. 163-178 (Lecture Notes in Computer Science, Bind 12666 ).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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TY - GEN
T1 - Latent Space Geometric Statistics
AU - Kühnel, Line
AU - Fletcher, Tom
AU - Joshi, Sarang
AU - Sommer, Stefan
N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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space pulls back to a nonlinear Riemannian geometry on latent space where classical linear statistical techniques are no longer applicable.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.
AB - 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.
U2 - 10.1007/978-3-030-68780-9_16
DO - 10.1007/978-3-030-68780-9_16
M3 - Article in proceedings
AN - SCOPUS:85103302449
SN - 9783030687793
T3 - Lecture Notes in Computer Science
SP - 163
EP - 178
BT - Pattern Recognition. ICPR International Workshops and Challenges, 2021, Proceedings
A2 - Del Bimbo, Alberto
A2 - Cucchiara, Rita
A2 - Sclaroff, Stan
A2 - Farinella, Giovanni Maria
A2 - Mei, Tao
A2 - Bertini, Marco
A2 - Escalante, Hugo Jair
A2 - Vezzani, Roberto
PB - Springer
T2 - 25th International Conference on Pattern Recognition Workshops, ICPR 2020
Y2 - 10 January 2021 through 15 January 2021
ER -
ID: 306680294