Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization
This work addresses scalable inference for Gaussian processes, which is a domain-specific problem, and appears incremental as it builds on existing variational and sparse approximation techniques.
The authors tackled scalable and accurate inference for latent Gaussian processes by proposing a variational approximation using Gaussian distributions with sparse inverse Cholesky factors, achieving polylogarithmic time per iteration and sometimes vastly more accuracy than alternative methods at similar computational complexity.
To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine this variational approximation of the posterior with a similar and efficient SIC-restricted Kullback-Leibler-optimal approximation of the prior. We then focus on a particular SIC ordering and nearest-neighbor-based sparsity pattern resulting in highly accurate prior and posterior approximations. For this setting, our variational approximation can be computed via stochastic gradient descent in polylogarithmic time per iteration. We provide numerical comparisons showing that the proposed double-Kullback-Leibler-optimal Gaussian-process approximation (DKLGP) can sometimes be vastly more accurate for stationary kernels than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.