Blackbox Matrix×Matrix Gaussian Process Inference

Despite numerous advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on recent trends in machine learning hardware. In this paper, we present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM uses a modified batched version of the conjugate gradients algorithm to derive all terms required for training and inference in a single call. Adapting this algorithm to complex models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM utilizes a specialized preconditioner that substantially speeds up convergence. In experiments, we show that BBMM efficiently utilizes GPU hardware, speeding up GP inference by an order of magnitude on a variety of popular GP models compared to existing approaches.