Parallel square-root statistical linear regression for inference in nonlinear state space models

TL;DR

This paper presents a parallel-in-time square-root statistical linear regression method for efficient and numerically stable inference in nonlinear state-space models, enabling fast parameter estimation and GPU implementation.

Contribution

It introduces a novel parallel-in-time square-root approach for nonlinear state-space inference, improving numerical stability and computational speed, especially for large datasets.

Findings

Achieves logarithmic time complexity for parameter estimation

Demonstrates improved numerical stability with square-root formulation

Shows practical efficiency on GPU hardware

Abstract

In this article, we introduce parallel-in-time methods for state and parameter estimation in general nonlinear non-Gaussian state-space models using the statistical linear regression and the iterated statistical posterior linearization paradigms. We also reformulate the proposed methods in a square-root form, resulting in improved numerical stability while preserving the parallelization capabilities. We then leverage the fixed-point structure of our methods to perform likelihood-based parameter estimation in logarithmic time with respect to the number of observations. Finally, we demonstrate the practical performance of the methodology with numerical experiments run on a graphics processing unit (GPU).