Fast Bayesian Matching Pursuit: Model Uncertainty and Parameter Estimation for Sparse Linear Models (2009)
| Venue: | IEEE TRANSACTIONS ON SIGNAL PROCESSING |
| Citations: | 9 - 2 self |
BibTeX
@MISC{Schniter09fastbayesian,
author = {Philip Schniter and Lee C. Potter and Justin Ziniel},
title = { Fast Bayesian Matching Pursuit: Model Uncertainty and Parameter Estimation for Sparse Linear Models},
year = {2009}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
A low-complexity recursive procedure is presented for model selection and minimum mean squared error (MMSE) estimation in linear regression. Emphasis is given to the case of a sparse parameter vector and fewer observations than unknown parameters. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both a set of high posterior probability mixing parameters and an approximate MMSE estimate of the parameter vector. Exact ratios of posterior probabilities serve to reveal potential ambiguity among multiple candidate solutions that are ambiguous due to observation noise or correlation among columns in the regressor matrix. Algorithm complexity is linear in the number of unknown coefficients, the number of observations and the number of nonzero coefficients. If hyperparameters are unknown, a maximum likelihood estimate is found by a generalized expectation maximization algorithm. Numerical simulations demonstrate estimation performance and illustrate the distinctions between MMSE estimation and maximum a posteriori probability model selection.
