Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classification

Juan Maroñas, Daniel Hernández-Lobato
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:24045-24081, 2023.

Abstract

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating $C$ stochastic processes characterized by: 1) the $C$ processes are non-stationary, 2) the $C$ processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point’s covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGP exploits the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGP, ETGP is constructed by transforming a single sample from a GP using $C$ invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGP, in general, outperforms state-of-the-art methods for multi-class classification based on GPs, and has a lower computational cost (around one order of magnitude smaller).

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-maronas23a, title = {Efficient Transformed {G}aussian Processes for Non-Stationary Dependent Multi-class Classification}, author = {Maro\~{n}as, Juan and Hern\'{a}ndez-Lobato, Daniel}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {24045--24081}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/maronas23a/maronas23a.pdf}, url = {https://proceedings.mlr.press/v202/maronas23a.html}, abstract = {This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating $C$ stochastic processes characterized by: 1) the $C$ processes are non-stationary, 2) the $C$ processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point’s covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGP exploits the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGP, ETGP is constructed by transforming a single sample from a GP using $C$ invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGP, in general, outperforms state-of-the-art methods for multi-class classification based on GPs, and has a lower computational cost (around one order of magnitude smaller).} }
Endnote
%0 Conference Paper %T Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classification %A Juan Maroñas %A Daniel Hernández-Lobato %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-maronas23a %I PMLR %P 24045--24081 %U https://proceedings.mlr.press/v202/maronas23a.html %V 202 %X This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating $C$ stochastic processes characterized by: 1) the $C$ processes are non-stationary, 2) the $C$ processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point’s covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGP exploits the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGP, ETGP is constructed by transforming a single sample from a GP using $C$ invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGP, in general, outperforms state-of-the-art methods for multi-class classification based on GPs, and has a lower computational cost (around one order of magnitude smaller).
APA
Maroñas, J. & Hernández-Lobato, D.. (2023). Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classification. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:24045-24081 Available from https://proceedings.mlr.press/v202/maronas23a.html.

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