# Online Variational Bayesian Subspace Filtering with Applications

## TL;DR

This paper introduces a Bayesian subspace filtering method for dynamic data recovery that automatically determines model complexity and outperforms existing matrix completion techniques in real-world applications.

## Contribution

It develops a variational Bayesian approach for time-varying subspace estimation with automatic relevance determination, reducing parameter tuning and computational complexity.

## Key findings

- Outperforms state-of-the-art matrix/tensor completion algorithms
- Effective in imputing missing data and rejecting outliers
- Demonstrates superior temporal prediction on real datasets

## Abstract

Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive approach of per-snapshot recovery is both expensive and sub-optimal. This paper develops generative Bayesian models that fit sequential multivariate measurements arising from a low-dimensional time-varying subspace. A variational Bayesian subspace filtering approach is proposed that learns the underlying subspace and its state-transition matrix. Different from the plethora of deterministic counterparts, the proposed approach utilizes automatic relevance determination priors that obviate the need to tune key parameters such as rank and noise power. We also propose a forward-backward algorithm that allows the updates to be carried out at low complexity. Extensive tests over traffic and electricity data demonstrate the superior imputation, outlier rejection, and temporal prediction prowess of the proposed algorithm over the state-of-the-art matrix/tensor completion algorithms.