Cramer-Rao-Type Bounds for Sparse Bayesian Learning

Prasad, Ranjitha and Murthy, Chandra R (2013) Cramer-Rao-Type Bounds for Sparse Bayesian Learning. In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, 61 (3).

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Abstract

In this paper, we derive Hybrid, Bayesian and Marginalized Cramer-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compressible Student-prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We extend the MCRB to the case where the compressible vector is distributed according to a general compressible prior distribution, of which the generalized Pareto distribution is a special case. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Further, we illustrate the tightness and utility of the bounds through simulations, by comparing them with the MSE performance of two popular SBL-based estimators. We find that the MCRB is generally the tightest among the bounds derived and that the MSE performance of the Expectation-Maximization (EM) algorithm coincides with the MCRB for the compressible vector. We also illustrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector for several values of the number of observations and at different signal powers.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON SIGNAL PROCESSING
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copyright for this article belongs to IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC,USA
Keywords:	Cramer-Rao lower bounds;expectation maximization;mean square error;sparse Bayesian learning
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	14 Mar 2013 09:47
Last Modified:	14 Mar 2013 09:47
URI:	http://eprints.iisc.ac.in/id/eprint/45995

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