Input Dependent Sparse Gaussian Processes

Bahram Jafrasteh, Carlos Villacampa-Calvo, Daniel Hernandez-Lobato
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:9739-9759, 2022.

Abstract

Gaussian Processes (GPs) are non-parametric models that provide accurate uncertainty estimates. Nevertheless, they have a cubic cost in the number of data instances $N$. To overcome this, sparse GP approximations are used, in which a set of $M \ll N$ inducing points is introduced. The location of the inducing points is learned by considering them parameters of an approximate posterior distribution $q$. Sparse GPs, combined with stochastic variational inference for inferring $q$ have a cost per iteration in $\mathcal{O}(M^3)$. Critically, the inducing points determine the flexibility of the model and they are often located in regions where the latent function changes. A limitation is, however, that in some tasks a large number of inducing points may be required to obtain good results. To alleviate this, we propose here to amortize the computation of the inducing points locations, as well as the parameters of $q$. For this, we use a neural network that receives a data instance as an input and outputs the corresponding inducing points locations and the parameters of $q$. We evaluate our method in several experiments, showing that it performs similar or better than other state-of-the-art sparse variational GPs. However, in our method the number of inducing points is reduced drastically since they depend on the input data. This makes our method scale to larger datasets and have faster training and prediction times.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-jafrasteh22a, title = {Input Dependent Sparse {G}aussian Processes}, author = {Jafrasteh, Bahram and Villacampa-Calvo, Carlos and Hernandez-Lobato, Daniel}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {9739--9759}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/jafrasteh22a/jafrasteh22a.pdf}, url = {https://proceedings.mlr.press/v162/jafrasteh22a.html}, abstract = {Gaussian Processes (GPs) are non-parametric models that provide accurate uncertainty estimates. Nevertheless, they have a cubic cost in the number of data instances $N$. To overcome this, sparse GP approximations are used, in which a set of $M \ll N$ inducing points is introduced. The location of the inducing points is learned by considering them parameters of an approximate posterior distribution $q$. Sparse GPs, combined with stochastic variational inference for inferring $q$ have a cost per iteration in $\mathcal{O}(M^3)$. Critically, the inducing points determine the flexibility of the model and they are often located in regions where the latent function changes. A limitation is, however, that in some tasks a large number of inducing points may be required to obtain good results. To alleviate this, we propose here to amortize the computation of the inducing points locations, as well as the parameters of $q$. For this, we use a neural network that receives a data instance as an input and outputs the corresponding inducing points locations and the parameters of $q$. We evaluate our method in several experiments, showing that it performs similar or better than other state-of-the-art sparse variational GPs. However, in our method the number of inducing points is reduced drastically since they depend on the input data. This makes our method scale to larger datasets and have faster training and prediction times.} }
Endnote
%0 Conference Paper %T Input Dependent Sparse Gaussian Processes %A Bahram Jafrasteh %A Carlos Villacampa-Calvo %A Daniel Hernandez-Lobato %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-jafrasteh22a %I PMLR %P 9739--9759 %U https://proceedings.mlr.press/v162/jafrasteh22a.html %V 162 %X Gaussian Processes (GPs) are non-parametric models that provide accurate uncertainty estimates. Nevertheless, they have a cubic cost in the number of data instances $N$. To overcome this, sparse GP approximations are used, in which a set of $M \ll N$ inducing points is introduced. The location of the inducing points is learned by considering them parameters of an approximate posterior distribution $q$. Sparse GPs, combined with stochastic variational inference for inferring $q$ have a cost per iteration in $\mathcal{O}(M^3)$. Critically, the inducing points determine the flexibility of the model and they are often located in regions where the latent function changes. A limitation is, however, that in some tasks a large number of inducing points may be required to obtain good results. To alleviate this, we propose here to amortize the computation of the inducing points locations, as well as the parameters of $q$. For this, we use a neural network that receives a data instance as an input and outputs the corresponding inducing points locations and the parameters of $q$. We evaluate our method in several experiments, showing that it performs similar or better than other state-of-the-art sparse variational GPs. However, in our method the number of inducing points is reduced drastically since they depend on the input data. This makes our method scale to larger datasets and have faster training and prediction times.
APA
Jafrasteh, B., Villacampa-Calvo, C. & Hernandez-Lobato, D.. (2022). Input Dependent Sparse Gaussian Processes. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:9739-9759 Available from https://proceedings.mlr.press/v162/jafrasteh22a.html.

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