Probabilistic sequential matrix factorization

TL;DR

The paper presents PSMF, a probabilistic method for factorizing high-dimensional, time-varying datasets using nonlinear Gaussian state-space models with efficient Kalman filtering, capable of handling nonlinearities and model misspecification.

Contribution

It introduces PSMF and its robust variant rPSMF, enabling efficient, nonlinear, and robust factorization of non-stationary time-series data with applications in various domains.

Findings

Effective modeling of time series with periodic subspaces.

Robust changepoint detection through rPSMF.

Successful imputation of missing high-dimensional data.

Abstract

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.