GPyTorch — Efficient Gaussian Processes in PyTorch

Introduction

GPyTorch is a Gaussian process library built on PyTorch that makes GP models as fast and scalable as deep neural networks. It uses GPU-accelerated linear algebra and modern approximation methods to handle datasets with millions of points, far beyond what traditional GP implementations can manage.

What GPyTorch Does

• Implements exact and approximate Gaussian process inference on GPU
• Provides a modular kernel library with automatic differentiation for hyperparameter learning
• Scales to datasets with millions of observations using KISS-GP and inducing point methods
• Integrates with BoTorch for Bayesian optimization and experiment design
• Supports multi-task, deep kernel, and variational Gaussian process models

Architecture Overview

GPyTorch represents GP models as PyTorch modules with lazy tensor operations. Kernel matrices are never fully materialized; instead, matrix-vector multiplies are computed on-the-fly using structured kernel interpolation (SKI) or inducing point methods. The CG (conjugate gradient) solver computes log-determinants and solves linear systems without forming dense matrices. Automatic differentiation through PyTorch handles hyperparameter optimization via type-II maximum likelihood.

Self-Hosting & Configuration

• Install via pip alongside PyTorch with GPU support
• Define custom GP models by subclassing gpytorch.models.ExactGP or ApproximateGP
• Choose kernels from the library or compose custom kernels with arithmetic operations
• Control CG solver tolerance and maximum iterations for speed-accuracy tradeoffs
• Use gpytorch.settings context managers to configure computation precision

Key Features

• GPU-accelerated kernel computations make GPs competitive with neural network training speed
• Lazy tensor algebra avoids materializing large kernel matrices in memory
• Modular design allows mixing kernels, likelihoods, and inference strategies
• Pre-conditioning strategies accelerate conjugate gradient convergence
• Tight integration with BoTorch enables production Bayesian optimization

Comparison with Similar Tools

• scikit-learn GaussianProcessRegressor — CPU-only with O(n^3) scaling; GPyTorch uses GPU and scales to millions of points
• GPflow — TensorFlow-based GP library; GPyTorch uses PyTorch and benefits from its autograd ecosystem
• BoTorch — Bayesian optimization library built on top of GPyTorch; GPyTorch provides the GP layer
• Stan — general probabilistic programming; GPyTorch specializes in GP models with GPU acceleration
• Pyro — deep probabilistic programming in PyTorch; GPyTorch focuses specifically on efficient GP inference

FAQ

Q: How many data points can GPyTorch handle? A: With approximate methods (KISS-GP, inducing points), GPyTorch scales to millions of data points on a single GPU.

Q: Can I use it for Bayesian optimization? A: Yes. GPyTorch is the GP backend for BoTorch, Meta's Bayesian optimization library used in production hyperparameter tuning.

Q: Does it support multi-output GPs? A: Yes. GPyTorch provides multi-task and multi-output GP models with shared or independent kernels.

Q: How does it compare to exact GP implementations? A: GPyTorch supports both exact inference (for smaller datasets) and scalable approximate inference for large datasets.

Sources

• https://github.com/cornellius-gp/gpytorch
• https://gpytorch.ai/