Learning GPLVM with arbitrary kernels using the unscented transformation

Daniel de Souza, Diego Mesquita, João Paulo Gomes, César Lincoln Mattos
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:451-459, 2021.

Abstract

Gaussian Process Latent Variable Model (GPLVM) is a flexible framework to handle uncertain inputs in Gaussian Processes (GPs) and incorporate GPs as components of larger graphical models. Nonetheless, the standard GPLVM variational inference approach is tractable only for a narrow family of kernel functions. The most popular implementations of GPLVM circumvent this limitation using quadrature methods, which may become a computational bottleneck even for relatively low dimensions. For instance, the widely employed Gauss-Hermite quadrature has exponential complexity on the number of dimensions. In this work, we propose using the unscented transformation instead. Overall, this method presents comparable, if not better, performance than off-the-shelf solutions to GPLVM, and its computational complexity scales only linearly on dimension. In contrast to Monte Carlo methods, our approach is deterministic and works well with quasi-Newton methods, such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. We illustrate the applicability of our method with experiments on dimensionality reduction and multistep-ahead prediction with uncertainty propagation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-souza21a, title = { Learning GPLVM with arbitrary kernels using the unscented transformation }, author = {de Souza, Daniel and Mesquita, Diego and Paulo Gomes, Jo\~{a}o and Lincoln Mattos, C{\'e}sar}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {451--459}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/souza21a/souza21a.pdf}, url = {https://proceedings.mlr.press/v130/souza21a.html}, abstract = { Gaussian Process Latent Variable Model (GPLVM) is a flexible framework to handle uncertain inputs in Gaussian Processes (GPs) and incorporate GPs as components of larger graphical models. Nonetheless, the standard GPLVM variational inference approach is tractable only for a narrow family of kernel functions. The most popular implementations of GPLVM circumvent this limitation using quadrature methods, which may become a computational bottleneck even for relatively low dimensions. For instance, the widely employed Gauss-Hermite quadrature has exponential complexity on the number of dimensions. In this work, we propose using the unscented transformation instead. Overall, this method presents comparable, if not better, performance than off-the-shelf solutions to GPLVM, and its computational complexity scales only linearly on dimension. In contrast to Monte Carlo methods, our approach is deterministic and works well with quasi-Newton methods, such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. We illustrate the applicability of our method with experiments on dimensionality reduction and multistep-ahead prediction with uncertainty propagation. } }
Endnote
%0 Conference Paper %T Learning GPLVM with arbitrary kernels using the unscented transformation %A Daniel de Souza %A Diego Mesquita %A João Paulo Gomes %A César Lincoln Mattos %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-souza21a %I PMLR %P 451--459 %U https://proceedings.mlr.press/v130/souza21a.html %V 130 %X Gaussian Process Latent Variable Model (GPLVM) is a flexible framework to handle uncertain inputs in Gaussian Processes (GPs) and incorporate GPs as components of larger graphical models. Nonetheless, the standard GPLVM variational inference approach is tractable only for a narrow family of kernel functions. The most popular implementations of GPLVM circumvent this limitation using quadrature methods, which may become a computational bottleneck even for relatively low dimensions. For instance, the widely employed Gauss-Hermite quadrature has exponential complexity on the number of dimensions. In this work, we propose using the unscented transformation instead. Overall, this method presents comparable, if not better, performance than off-the-shelf solutions to GPLVM, and its computational complexity scales only linearly on dimension. In contrast to Monte Carlo methods, our approach is deterministic and works well with quasi-Newton methods, such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. We illustrate the applicability of our method with experiments on dimensionality reduction and multistep-ahead prediction with uncertainty propagation.
APA
de Souza, D., Mesquita, D., Paulo Gomes, J. & Lincoln Mattos, C.. (2021). Learning GPLVM with arbitrary kernels using the unscented transformation . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:451-459 Available from https://proceedings.mlr.press/v130/souza21a.html.

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