2019/10/09 by Ömer Deniz Akyıldız, Ömer Deniz Akyildiz, Gerrit J. J. van den Burg +6
Computer Science · Mathematics · #Algorithm #Artificial intelligence #Bayesian inference #Bayesian probability #Blind Source Separation Techniques #Computation (stat.CO) #Computer science #FOS: Computer and information sciences #Factorization #Gaussian Processes and Bayesian Inference #Inference #Kalman filter #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematics #Matrix (chemical analysis) #Matrix decomposition #Nonlinear system #Probabilistic logic #Series (stratigraphy) #State space #Statistical and numerical algorithms #Subspace topology #cs.LG #stat.CO #stat.ML
paper · pdf · doi:10.48550/arxiv.1910.03906
published in arXiv (Cornell University) (Cornell University) · Accepted for publication at AISTATS 2021
openalex publication_date 2019/10/09 · arxiv created 2021/03/18 · arxiv updated 2021/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space models where sequential approximate inference results in the factorization of a data matrix into a dictionary and time-varying coefficients with potentially nonlinear Markovian dependencies. The assumed Markovian structure on the coefficients enables us to encode temporal dependencies into a low-dimensional feature space. The proposed inference method is solely based on an approximate extended Kalman filtering scheme, which makes the resulting method particularly efficient. PSMF can account for temporal nonlinearities and, more importantly, can be used to calibrate and estimate generic differentiable nonlinear subspace models. We also introduce a robust version of PSMF, called rPSMF, which uses Student-t filters to handle model misspecification. We show that PSMF can be used in multiple contexts: modeling time series with a periodic subspace, robustifying changepoint detection methods, and imputing missing data in several high-dimensional time-series, such as measurements of pollutants across London.