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

2026-07-22 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Environmental Science & Earth Systems · Depth: Expert, extended

Summary

A new Fast Multivariate Ornstein-Uhlenbeck (FMOU) approach is introduced for scalable data inversion in high-dimensional dynamical systems with noisy measurements. This method utilizes a flexible latent factor model where each factor has distinct correlation and variance parameters, and an orthogonal factor loading matrix. The core innovation is a novel expectation-maximization (EM) algorithm that provides closed-form expressions for all parameter estimations, including the factor loading matrix, correlation, and variance parameters. This design avoids computationally intensive large matrix inversions typically required in Kalman filters, leading to substantial computational acceleration. Applied to geodetic data from the Cascadia region, FMOU demonstrated higher accuracy and was 300-3000 times faster than alternative methods like Network Inversion Filter (NIF) and modified NIF, improving the estimation of slow slip events and their correlation with seismic tremor events.

Key takeaway

For geophysicists and ML engineers working with high-dimensional time-series data and noisy observations, you should consider adopting the FMOU approach. Its demonstrated 300-3000x speedup and higher accuracy in real-world applications like Cascadia slow slip event detection mean you can process massive datasets more efficiently and gain more reliable insights into complex dynamic systems, enabling better hazard quantification.

Key insights

FMOU offers a fast, scalable EM algorithm with closed-form solutions for high-dimensional noisy dynamical systems.

Principles

• Orthogonal factor loading matrices avoid large matrix inversions.
• Closed-form EM expressions enhance estimation stability and speed.
• Distinct parameters for each latent factor increase model flexibility.

Method

The FMOU algorithm uses an EM framework with Kalman filter and RTS smoother to compute quantities. It derives closed-form updates for all parameters, including the orthogonal factor loading matrix, correlation, and variance, avoiding numerical optimization.

In practice

• Apply FMOU for efficient fault slip estimation from GPS data.
• Use variance matching to select the optimal number of latent factors.
• Integrate orthogonal projection in Kalman filters to bypass matrix inversion.

Topics

• Ornstein-Uhlenbeck Process
• Latent Factor Models
• Expectation-Maximization Algorithm
• Kalman Filter
• Geodetic Data Inversion
• Slow Slip Events

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.