# Hierarchical Non-Stationary Temporal Gaussian Processes With L1-Regularization

arXiv: https://arxiv.org/abs/2105.09695 · HTML: https://mlsanity.com/paper/2105.09695/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 20 May 2021.

## Builds on (most cited first, 17 of 17)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges](https://mlsanity.com/paper/2006.09319/) (2020)
- [Linearly constrained Gaussian processes](https://mlsanity.com/paper/1703.00787/) (2017)
- [Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1508.04319/) (2015)
- [Modeling and interpolation of the ambient magnetic field by Gaussian processes](https://mlsanity.com/paper/1509.04634/) (2015)
- [Learning Scalable Deep Kernels with Recurrent Structure](https://mlsanity.com/paper/1610.08936/) (2016)
- [Algorithmic Linearly Constrained Gaussian Processes](https://mlsanity.com/paper/1801.09197/) (2018)
- [Gaussian process emulators for computer experiments with inequality constraints](https://mlsanity.com/paper/1606.01265/) (2016)
- [Gaussian processes with linear operator inequality constraints](https://mlsanity.com/paper/1901.03134/) (2019)
- [Deep State-Space Gaussian Processes](https://mlsanity.com/paper/2008.04733/) (2020)
- [Iterated Extended Kalman Smoother-based Variable Splitting for L1-Regularized State Estimation](https://mlsanity.com/paper/1903.08605/) (2019)
- [Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering and Smoothing](https://mlsanity.com/paper/2001.02466/) (2020)
- [Variable Splitting Methods for Constrained State Estimation in Partially Observed Markov Processes](https://mlsanity.com/paper/2005.08275/) (2020)

## Built on by (most cited first, 1 of 1)

- [State-space deep Gaussian processes with applications](https://mlsanity.com/paper/2111.12604/) (2021)

## Abstract (arXiv)

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 L1-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.