Article

Fast Variational Sparse Bayesian Learning With Automatic Relevance Determination for Superimposed Signals

Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA
IEEE Transactions on Signal Processing (Impact Factor: 3.2). 01/2012; DOI: 10.1109/TSP.2011.2168217
Source: IEEE Xplore

ABSTRACT In this work, a new fast variational sparse Bayesian learning (SBL) approach with automatic relevance determination (ARD) is proposed. The sparse Bayesian modeling, exemplified by the relevance vector machine (RVM), allows a sparse regression or classification function to be constructed as a linear combination of a few basis functions. It is demonstrated that, by computing the stationary points of the variational update expressions with noninformative (ARD) hyperpriors, a fast version of variational SBL can be constructed. Analysis of the computed stationary points indicates that SBL with Gaussian sparsity priors and noninformative hyperpriors corresponds to removing components with signal-to-noise ratio below a 0 dB threshold; this threshold can also be adjusted to significantly improve the convergence rate and sparsity of SBL. It is demonstrated that the pruning conditions derived for fast variational SBL coincide with those obtained for fast marginal likelihood maximization; moreover, the parameters that maximize the variational lower bound also maximize the marginal likelihood function. The effectiveness of fast variational SBL is demonstrated with synthetic as well as with real data.

0 Followers
 · 
271 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: The Sparse Bayesian learning (SBL) framework has been successfully adopted for sparse signal recovery. In SBL inference can be performed either via Type-II Maximum Likelihood or by following a Variational approach. When employing uninformative prior distributions, fast algorithms have been proposed for both renditions of SBL and it has been proven that they are equivalent. Unfortunately the use of such priors prohibits the incorporation of prior statistical information which can be beneficial in terms of convergence and accuracy. A modified variational approach is proposed, resulting in a fast variational algorithm for informative priors. A fixed point analysis is performed with the major challenge being the highly involved analytical expressions for the points in the fixed set. The given theoretical analysis demonstrates how this issue can be circumvented. Comprehensive empirical results are given to support the claims.
    ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 05/2014
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper a novel algorithm for estimation and tracking of multipath components for range estimation using signals with low bandwidth is discussed. In multipath rich environments ranging becomes a challenging problem when used with low bandwidth signals: unless multipath interference is resolved, large ranging errors are typical. In this work the estimation and tracking of individual multipath components is studied. The new technique combines sparse Bayesian learning and variational Bayesian parameter estimation with Kalman filtering. While the former is used to detect and estimate the individual components, the Kalman filtering is used to track the estimated signals. Two assumptions are compared: independence of multipath components, typical for classical multipath estimation schemes, versus correlation between the propagation paths. The later has been found to improve component tracking and estimation at the cost of increased computational complexity. The performance of the algorithm is investigated using synthetic, as well as real measurement data collected during flight trials. Significantly improved ranging performance can be obtained as compared to the standard correlation-based ranging.
    IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Florence, Italy; 05/2014
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents an online version of the widely used sparse Bayesian learning (SBL) algorithm. Exploiting the variational Bayes framework, an efficient online SBL algorithm is constructed, that acts as a fully automatic learning method for the adaptive estimation of sparse time-varying signals. The new method is based on second order statistics and comprises a simple, automated sparsity-imposing mechanism, different from that of other known schemes. The effectiveness of the proposed online Bayesian algorithm is illustrated using experimental results conducted on synthetic data. These results show that the proposed scheme achieves faster initial convergence and superior estimation performance compared to other related state-of-the-art schemes.
    ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 05/2014