GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration

TL;DR

GPyTorch introduces a GPU-accelerated, blackbox matrix-matrix approach for Gaussian process inference that significantly reduces computational complexity and accelerates both exact and approximate inference methods.

Contribution

The paper presents BBMM, a novel GPU-based inference method for GPs that reduces complexity and improves speed, implemented in the GPyTorch software platform.

Findings

BBMM reduces GP inference complexity from O(n^3) to O(n^2).

GPU acceleration dramatically speeds up exact and approximate GP inference.

GPyTorch enables scalable Gaussian process inference with hardware acceleration.

Abstract

Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched version of the conjugate gradients algorithm to derive all terms for training and inference in a single call. BBMM reduces the asymptotic complexity of exact GP inference from $O(n^3)$ to $O(n^2)$. Adapting this algorithm to scalable approximations and complex GP models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM uses a specialized preconditioner to substantially speed up convergence. In experiments we show that BBMM effectively uses GPU hardware to dramatically accelerate both exact GP inference and scalable approximations. Additionally, we provide GPyTorch, a software platform for scalable GP inference via BBMM, built on PyTorch.