Departmental Papers (ESE)


We propose a Bayesian framework for learning the optimal regularization parameter in the L1-norm penalized least-mean-square (LMS) problem, also known as LASSO [1] or basis pursuit [2]. The setting of the regularization parameter is critical for deriving a correct solution. In most existing methods, the scalar regularization parameter is often determined in a heuristic manner; in contrast, our approach infers the optimal regularization setting under a Bayesian framework. Furthermore, Bayesian inference enables an independent regularization scheme where each coefficient (or weight) is associated with an independent regularization parameter. Simulations illustrate the improvement using our method in discovering sparse structure from noisy data.

Document Type

Conference Paper

Subject Area


Date of this Version

May 2006


Copyright 2006 IEEE. Reprinted from Proceedings of the 2006 IEEE International Conference Acoustics, Speech and Signal Processing, Volume 5, pages V605-V608. Publisher URL:

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Date Posted: 16 April 2007

This document has been peer reviewed.