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This paper is concerned with regularized extensions of hierarchicalnon-stationary temporal Gaussian processes (NSGPs) in which the parameters(e.g., length-scale) are modeled as GPs. In particular, we consider twocommonly used NSGP constructions which are based on explicitly constructednon-stationary covariance functions and stochastic differential equations,respectively. We extend these NSGPs by including $L^1$-regularization on theprocesses in order to induce sparseness. To solve the resulting regularizedNSGP (R-NSGP) regression problem we develop a method based on the alternatingdirection method of multipliers (ADMM) and we also analyze its convergenceproperties theoretically. We also evaluate the performance of the proposedmethods in simulated and real-world datasets.

Hierarchical Non-Stationary Temporal Gaussian Processes With $L^1$-Regularization