Sparse Gaussian Processes with Spherical Harmonic Features

Abstract

We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations. Our inference scheme is comparable to variational Fourier features, but it does not suffer from the curse of dimensionality, and leads to diagonal covariance matrices between inducing variables. This enables a speed-up in inference, because it bypasses the need to invert large covariance matrices. Our experiments show that our model is able to fit a regression model for a dataset with 6 million entries two orders of magnitude faster compared to standard sparse GPs, while retaining state of the art accuracy. We also demonstrate competitive performance on classification with non-conjugate likelihoods.

International Conference on Machine, PMLR 119, 2020

Cited by in corpus (13)

• A Tutorial on Sparse Gaussian Processes and Variational Inference
• Scalable Gaussian Processes on Discrete Domains
• Transforming Gaussian Processes With Normalizing Flows
• Scalable Thompson Sampling using Sparse Gaussian Process Models
• SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data
• Matérn Gaussian Processes on Graphs
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition
• Deep Neural Networks as Point Estimates for Deep Gaussian Processes
• Conditional Deep Gaussian Processes: empirical Bayes hyperdata learning
• Spectrum Gaussian Processes Based On Tunable Basis Functions
• Sparse Algorithms for Markovian Gaussian Processes
• Large-Scale Learning with Fourier Features and Tensor Decompositions
• Uniform Generalization Bounds for Overparameterized Neural Networks