Constant-Time Predictive Distributions for Gaussian Processes
arXiv:1803.06058
Abstract
One of the most compelling features of Gaussian process (GP) regression is its ability to provide well-calibrated posterior distributions. Recent advances in inducing point methods have sped up GP marginal likelihood and posterior mean computations, leaving posterior covariance estimation and sampling as the remaining computational bottlenecks. In this paper we address these shortcomings by using the Lanczos algorithm to rapidly approximate the predictive covariance matrix. Our approach, which we refer to as LOVE (LanczOs Variance Estimates), substantially improves time and space complexity. In our experiments, LOVE computes covariances up to 2,000 times faster and draws samples 18,000 times faster than existing methods, all without sacrificing accuracy.
ICML 2018
References in corpus (8)
- Practical Bayesian Optimization of Machine Learning Algorithms
- Towards A Rigorous Science of Interpretable Machine Learning
- Predictive Entropy Search for Efficient Global Optimization of Black-box Functions
- Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
- Max-value Entropy Search for Efficient Bayesian Optimization
- Stochastic Variational Deep Kernel Learning
- Product Kernel Interpolation for Scalable Gaussian Processes
- Scalable Log Determinants for Gaussian Process Kernel Learning
Cited by in corpus (6)
- GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration
- On Random Subsampling of Gaussian Process Regression: A Graphon-Based Analysis
- Bayesian Optimization with High-Dimensional Outputs
- Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models
- Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees
- Scalable Gaussian Processes for Predicting the Properties of Inorganic Glasses with Large Datasets