Variational nearest neighbor Gaussian process

Luhuan Wu, Geoff Pleiss, John P Cunningham
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:24114-24130, 2022.

Abstract

Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix. We propose variational nearest neighbor Gaussian process (VNNGP), which introduces a prior that only retains correlations within $K$ nearest-neighboring observations, thereby inducing sparse precision structure. Using the variational framework, VNNGP’s objective can be factorized over both observations and inducing points, enabling stochastic optimization with a time complexity of $O(K^3)$. Hence, we can arbitrarily scale the inducing point size, even to the point of putting inducing points at every observed location. We compare VNNGP to other scalable GPs through various experiments, and demonstrate that VNNGP (1) can dramatically outperform low-rank methods, and (2) is less prone to overfitting than other nearest neighbor methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-wu22h, title = {Variational nearest neighbor {G}aussian process}, author = {Wu, Luhuan and Pleiss, Geoff and Cunningham, John P}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {24114--24130}, 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/wu22h/wu22h.pdf}, url = {https://proceedings.mlr.press/v162/wu22h.html}, abstract = {Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix. We propose variational nearest neighbor Gaussian process (VNNGP), which introduces a prior that only retains correlations within $K$ nearest-neighboring observations, thereby inducing sparse precision structure. Using the variational framework, VNNGP’s objective can be factorized over both observations and inducing points, enabling stochastic optimization with a time complexity of $O(K^3)$. Hence, we can arbitrarily scale the inducing point size, even to the point of putting inducing points at every observed location. We compare VNNGP to other scalable GPs through various experiments, and demonstrate that VNNGP (1) can dramatically outperform low-rank methods, and (2) is less prone to overfitting than other nearest neighbor methods.} }
Endnote
%0 Conference Paper %T Variational nearest neighbor Gaussian process %A Luhuan Wu %A Geoff Pleiss %A John P Cunningham %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-wu22h %I PMLR %P 24114--24130 %U https://proceedings.mlr.press/v162/wu22h.html %V 162 %X Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix. We propose variational nearest neighbor Gaussian process (VNNGP), which introduces a prior that only retains correlations within $K$ nearest-neighboring observations, thereby inducing sparse precision structure. Using the variational framework, VNNGP’s objective can be factorized over both observations and inducing points, enabling stochastic optimization with a time complexity of $O(K^3)$. Hence, we can arbitrarily scale the inducing point size, even to the point of putting inducing points at every observed location. We compare VNNGP to other scalable GPs through various experiments, and demonstrate that VNNGP (1) can dramatically outperform low-rank methods, and (2) is less prone to overfitting than other nearest neighbor methods.
APA
Wu, L., Pleiss, G. & Cunningham, J.P.. (2022). Variational nearest neighbor Gaussian process. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:24114-24130 Available from https://proceedings.mlr.press/v162/wu22h.html.

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