# A Probabilistic Least-Mean-Squares Filter

arXiv: https://arxiv.org/abs/1501.06929 · HTML: https://mlsanity.com/paper/1501.06929/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2015.

## Built on by (most cited first, 1 of 1)

- [Distributed adaptive algorithm based on the asymmetric cost of error functions](https://mlsanity.com/paper/2107.03067/) (2021)

## Abstract (arXiv)

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.