Isometric Gaussian Process Latent Variable Model for Dissimilarity Data

Martin Jørgensen, Soren Hauberg
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:5127-5136, 2021.

Abstract

We present a probabilistic model where the latent variable respects both the distances and the topology of the modeled data. The model leverages the Riemannian geometry of the generated manifold to endow the latent space with a well-defined stochastic distance measure, which is modeled locally as Nakagami distributions. These stochastic distances are sought to be as similar as possible to observed distances along a neighborhood graph through a censoring process. The model is inferred by variational inference based on observations of pairwise distances. We demonstrate how the new model can encode invariances in the learned manifolds.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-jorgensen21a, title = {Isometric Gaussian Process Latent Variable Model for Dissimilarity Data}, author = {J{\o}rgensen, Martin and Hauberg, Soren}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {5127--5136}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/jorgensen21a/jorgensen21a.pdf}, url = {https://proceedings.mlr.press/v139/jorgensen21a.html}, abstract = {We present a probabilistic model where the latent variable respects both the distances and the topology of the modeled data. The model leverages the Riemannian geometry of the generated manifold to endow the latent space with a well-defined stochastic distance measure, which is modeled locally as Nakagami distributions. These stochastic distances are sought to be as similar as possible to observed distances along a neighborhood graph through a censoring process. The model is inferred by variational inference based on observations of pairwise distances. We demonstrate how the new model can encode invariances in the learned manifolds.} }
Endnote
%0 Conference Paper %T Isometric Gaussian Process Latent Variable Model for Dissimilarity Data %A Martin Jørgensen %A Soren Hauberg %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-jorgensen21a %I PMLR %P 5127--5136 %U https://proceedings.mlr.press/v139/jorgensen21a.html %V 139 %X We present a probabilistic model where the latent variable respects both the distances and the topology of the modeled data. The model leverages the Riemannian geometry of the generated manifold to endow the latent space with a well-defined stochastic distance measure, which is modeled locally as Nakagami distributions. These stochastic distances are sought to be as similar as possible to observed distances along a neighborhood graph through a censoring process. The model is inferred by variational inference based on observations of pairwise distances. We demonstrate how the new model can encode invariances in the learned manifolds.
APA
Jørgensen, M. & Hauberg, S.. (2021). Isometric Gaussian Process Latent Variable Model for Dissimilarity Data. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:5127-5136 Available from https://proceedings.mlr.press/v139/jorgensen21a.html.

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