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

TL;DR

This paper introduces regularized hierarchical non-stationary temporal Gaussian processes with L1-regularization to induce sparsity, solved via ADMM, and demonstrates their effectiveness on simulated and real data.

Contribution

It extends existing NSGP models with L1-regularization and develops an ADMM-based solution with theoretical convergence analysis.

Findings

Effective sparsity induction in NSGPs.

Successful application to real-world datasets.

Theoretical convergence guarantees for the proposed method.

Abstract

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