Variational Orthogonal Features

David R. Burt; Carl Edward Rasmussen; Mark van der Wilk

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arXiv · 2006.13170

Variational Orthogonal Features

David R. Burt·Carl Edward Rasmussen·Mark van der Wilk

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Abstract

Sparse stochastic variational inference allows Gaussian process models to be applied to large datasets. The per iteration computational cost of inference with this method is $\mathcal{O}(\tilde{N}M^2+M^3),$ where $\tilde{N}$ is the number of points in a minibatch and $M$ is the number of `inducing features', which determine the expressiveness of the variational family. Several recent works have shown that for certain priors, features can be defined that remove the $\mathcal{O}(M^3)$ cost of computing a minibatch estimate of an evidence lower bound (ELBO). This represents a significant computational savings when $M\gg \tilde{N}$. We present a construction of features for any stationary prior kernel that allow for computation of an unbiased estimator to the ELBO using $T$ Monte Carlo samples in $\mathcal{O}(\tilde{N}T+M^2T)$ and in $\mathcal{O}(\tilde{N}T+MT)$ with an additional approximation. We analyze the impact of this additional approximation on inference quality.

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David R. Burt, Carl Edward Rasmussen, Mark van der Wilk. 2020-06-23. Variational Orthogonal Features. https://arxiv.org/abs/2006.13170

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