# Fast data inversion for high-dimensional Ornstein-Uhlenbeck processes from noisy measurements

arXiv: https://arxiv.org/abs/2501.01324 · HTML: https://mlsanity.com/paper/2501.01324/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 41 references that are in the map.
- First posted on arXiv 2 Jan 2025.

## Builds on (most cited first, 3 of 3)

- [Generalized probabilistic principal component analysis of correlated data](https://mlsanity.com/paper/1808.10868/) (2018)
- [Probabilistic forecast of nonlinear dynamical systems with uncertainty quantification](https://mlsanity.com/paper/2305.08942/) (2023)
- [Ab initio uncertainty quantification in scattering analysis of microscopy](https://mlsanity.com/paper/2309.02468/) (2023)

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

- [Unsupervised cell segmentation by fast Gaussian Processes](https://mlsanity.com/paper/2505.18902/) (2025)

## Abstract (arXiv)

In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can be either fixed or estimated. We utilize an orthogonal factor loading matrix that avoids computing the inversion of the posterior covariance matrix at each time of the Kalman filter, and derive closed-form expressions in an expectation-maximization algorithm for parameter estimation, which substantially reduces the computational complexity without approximation. Our approach has several applications, including noise filtering for high-dimensional time series, estimating nonseparable covariance structure between different time series, and estimating latent physical processes from real-world measurements. Extensive simulated studies illustrate higher accuracy and scalability of our approach compared to alternatives. Furthermore, by applying our method to geodetic measurements to estimate slow slip events from geodetic data in the Cascadia region, our estimated slip better agrees with independently measured seismic data of tremor events. The substantial acceleration from our method enables the use of massive noisy data for geological hazard quantification and other applications.