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.

翻译：为实现可扩展且精确的潜在高斯过程推理，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。我们将后验的变分近似与先验的相似且高效的SIC约束下KL最优近似相结合。随后聚焦于特定SIC排序和基于最近邻的稀疏模式，该模式能实现高度精确的先验与后验近似。在此设定下，我们的变分近似可通过每次迭代的多对数时间阶随机梯度下降进行计算。数值比较表明，所提出的双KL最优高斯过程近似（DKLGP）在固定核函数下，其计算复杂度与诱导点及平均场近似等方法相近，但有时可达到远超后者的精度。