  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.
