Learning Compositional Sparse Gaussian Processes with a Shrinkage Prior
This work provides a faster and more efficient method for learning compositional Gaussian Process kernels, which is beneficial for researchers and practitioners working with large-scale time series data.
This paper addresses the slow kernel composition learning in Gaussian Process (GP) models, especially for large-scale data. They propose MultiSVGP, a new sparse approximate posterior, and a probabilistic algorithm using a Horseshoe prior to learn kernel compositions. The model significantly reduces computational time while maintaining competitive regression performance on real-world time series datasets.
Choosing a proper set of kernel functions is an important problem in learning Gaussian Process (GP) models since each kernel structure has different model complexity and data fitness. Recently, automatic kernel composition methods provide not only accurate prediction but also attractive interpretability through search-based methods. However, existing methods suffer from slow kernel composition learning. To tackle large-scaled data, we propose a new sparse approximate posterior for GPs, MultiSVGP, constructed from groups of inducing points associated with individual additive kernels in compositional kernels. We demonstrate that this approximation provides a better fit to learn compositional kernels given empirical observations. We also provide theoretically justification on error bound when compared to the traditional sparse GP. In contrast to the search-based approach, we present a novel probabilistic algorithm to learn a kernel composition by handling the sparsity in the kernel selection with Horseshoe prior. We demonstrate that our model can capture characteristics of time series with significant reductions in computational time and have competitive regression performance on real-world data sets.