Probabilistic sequential matrix factorization
This work addresses the challenge of modeling complex temporal data in domains like environmental monitoring, though it appears incremental as an extension of existing matrix factorization methods.
The authors tackled the problem of factorizing high-dimensional, time-varying, and non-stationary datasets by introducing probabilistic sequential matrix factorization (PSMF), which uses nonlinear Gaussian state-space models and approximate extended Kalman filtering to efficiently encode temporal dependencies into a low-dimensional feature space, with applications including pollutant measurement imputation in London.
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.