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 than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.

翻译：为实现潜在高斯过程的可扩展且精确推断，我们提出一种基于协方差矩阵具有稀疏逆乔列斯基（SIC）因子的高斯分布族的变分近似方法。我们将这种后验的变分近似与一种类似且高效的SIC约束下的KL散度最优先验近似相结合。进一步聚焦于特定SIC排序及基于最近邻的稀疏模式，从而获得高度精确的先验与后验近似。在该设定下，我们的变分近似可通过随机梯度下降在每次迭代的对数多项式时间内完成计算。数值比较表明，所提出的双重KL散度最优高斯过程近似（DKLGP）在相似计算复杂度下，有时可显著优于诱导点近似和平均场近似等替代方法。