Sparse Inverse Gaussian Process Regression with Application to Climate Network Discovery

Such interpretable sparsity patterns are very important for many applications. We propose a new technique for sparse Gaussian Process regression that allows us to compute a parsimonious model while preserving the interpretability of the sparsity structure in the data. We discuss how the inverse kernel matrix used in Gaussian Process prediction gives valuable domain information and then adapt the inverse covariance estimation from Gaussian graphical models to estimate the Gaussian kernel.

We solve the optimization problem using the alternating direction method of multipliers that is amenable to parallel computation. We demonstrate the performance of our method in terms of accuracy, scalability and interpretability on a climate data set.