A Probabilistic Least-Mean-Squares Filter

TL;DR

This paper presents a probabilistic LMS filter that adapts step-size and quantifies uncertainty, improving performance while maintaining linear complexity, and aims to integrate Bayesian methods into adaptive filtering.

Contribution

It introduces a probabilistic approach to LMS filtering with an efficient approximation, enabling adaptive step-size and uncertainty measurement without increasing complexity.

Findings

Enhanced performance over standard LMS

Comparable complexity to existing algorithms

Provides uncertainty estimates in filtering

Abstract

We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the proposed approximation preserves the linear complexity of the standard LMS. Numerical results show the improved performance of the algorithm with respect to standard LMS and state-of-the-art algorithms with similar complexity. The goal of this work, therefore, is to open the door to bring some more Bayesian machine learning techniques to adaptive filtering.