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

arXiv: https://arxiv.org/abs/2207.00426 · HTML: https://mlsanity.com/paper/2207.00426/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2022.

## Built on by (most cited first, 6 of 6)

- [A Unifying Framework for Parallelizing Sequential Models with Linear Dynamical Systems](https://mlsanity.com/paper/2509.21716/) (2025)
- [Parallel-in-Time Probabilistic Numerical ODE Solvers](https://mlsanity.com/paper/2310.01145/) (2023)
- [Numerically Robust Fixed-Point Smoothing Without State Augmentation](https://mlsanity.com/paper/2409.20004/) (2024)
- [Auxiliary MCMC and particle Gibbs samplers for parallelisable inference in latent dynamical systems](https://mlsanity.com/paper/2303.00301/) (2023)
- [Recursive Entropic Variational Inference for Nonlinear State-Space Models](https://mlsanity.com/paper/2511.15409/) (2025)
- [Robust Automatic Differentiation of Square-Root Kalman Filters via Gramian Differentials](https://mlsanity.com/paper/2603.13559/) (2026)

## Abstract (arXiv)

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).