Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization

LGPs extend GPs to a large class of settings, including noisy, categorical, and count data. However, To achieve scalable and accurate inference for LGP inference is generally analytically intractable and latent Gaussian processes, we propose a variational hence requires approximations. In addition, direct GP inference approximation based on a family of Gaussian is prohibitive for large datasets due to cubic scaling distributions whose covariance matrices have in the data size. There are two main challenges for (L)GPs sparse inverse Cholesky (SIC) factors. We combine in many applications: One is to specify or learn a suitable this variational approximation of the posterior kernel for the GP, and the other is carrying out fast inference with a similar and efficient SIC-restricted for a given kernel. In this paper, we make no contributions Kullback-Leibler-optimal approximation of the to the former and instead focus on the latter challenge: We prior. We then focus on a particular SIC ordering assume that a parametric kernel form is given and propose and nearest-neighbor-based sparsity pattern an efficient approximation method for LGP inference via resulting in highly accurate prior and posterior structured variational learning.