Online Variational Bayesian Subspace Filtering

Abstract

Many real world applications that suffer from missing data and outliers can be modeled in a matrix completion framework. In this paper, we consider low-rank matrices whose subspace evolves according to a state-space model and propose an online variational Bayesian formulation to learn the low rank components as well as the state-space model. Unlike the other matrix/tensor completion techniques, in our framework, the key algorithm parameters like rank and various noise power need not be fine-tuned and are learned automatically. We also propose a forward-backward algorithm that allows update to be carried out at low complexity manner. Simulations performed on the real world traffic data illustrates promising imputation as well as temporal prediction performance even in an online setup.