Hierarchical Non-Stationary Temporal Gaussian Processes With $L^1$-Regularization
This work addresses the need for sparse and interpretable models in time-series analysis, but it is incremental as it builds on existing non-stationary Gaussian process frameworks.
The paper tackled the problem of modeling non-stationary temporal data by extending hierarchical non-stationary Gaussian processes with L1-regularization to induce sparsity, and developed an ADMM-based method to solve the regression problem, evaluating it on simulated and real-world datasets.
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.