Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


ParkerJasonTDissertation.pdf (3.05 MB)

ETD Abstract Container

Abstract Header

Approximate Message Passing Algorithms for Generalized Bilinear Inference

Parker, Jason Terry
http://rave.ohiolink.edu/etdc/view?acc_num=osu1405690178

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
Recent developments in compressive sensing (CS) combined with increasing demands for effective high-dimensional inference techniques across a variety of disciplines have motivated extensive research into algorithms exploiting various notions of parsimony, including sparsity and low-rank constraints. In this dissertation, we extend the generalized approximate message passing (GAMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of CS, to handle several classes of bilinear inference problems. First, we consider a general form of noisy CS where there is uncertainty in the measurement matrix as well as in the measurements. Matrix uncertainty is motivated by practical cases in which there are imperfections or unknown calibration parameters in the signal acquisition hardware. While previous work has focused on analyzing and extending classical CS algorithms like the LASSO and Dantzig selector for this problem setting, we propose a new algorithm called Matrix Uncertain GAMP (MU-GAMP) whose goal is minimization of mean-squared error of the signal estimates in the presence of these uncertainties, without attempting to estimate the uncertain measurement matrix itself. Next, we extend GAMP to the generalized-bilinear case, in which the measurement matrix is estimated jointly with the signals of interest, enabling its application to matrix completion, robust PCA, dictionary learning, and related matrix-factorization problems. We derive this Bilinear GAMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, where central limit theorem arguments and Taylor-series approximations apply, and under the assumption of statistically independent matrix entries with known priors. In addition, we propose an adaptive damping mechanism that aids convergence under finite problem sizes, an expectation-maximization (EM)-based method to automatically tune the parameters of the assumed priors, and two rank-selection strategies. We then discuss the specializations of EM-BiG-AMP to the problems of matrix completion, robust PCA, and dictionary learning, and present the results of an extensive empirical study comparing EM-BiG-AMP to state-of-the-art algorithms on each problem. Our numerical results, using both synthetic and real-world datasets, demonstrate that EM-BiG-AMP yields excellent reconstruction accuracy (often best in class) while maintaining competitive runtimes and avoiding the need to tune algorithmic parameters. Finally, we propose a parametric extension known as P-BiG-AMP, which recovers BiG-AMP as a special case, that relaxes the assumption of statistically independent matrix entries by introducing parametric models for the two matrix factors. The resulting algorithm is rigorously justified for random affine parameterizations and constructed to allow its use with an even wider class of non-linear parameterizations, enabling numerous potential applications.
Philip Schniter (Advisor)
Lee Potter (Committee Member)
Emre Ertin (Committee Member)
204 p.
Electrical Engineering
compressed sensing; compressive sensing; approximate message passing; matrix uncertainty; bilinear inference; matrix completion; robust principal components analysis; dictionary learning

Recommended Citations

Citations

  • Parker, J. T. (2014). Approximate Message Passing Algorithms for Generalized Bilinear Inference [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1405690178

    APA Style (7th edition)

  • Parker, Jason. Approximate Message Passing Algorithms for Generalized Bilinear Inference . 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1405690178.

    MLA Style (8th edition)

  • Parker, Jason. "Approximate Message Passing Algorithms for Generalized Bilinear Inference ." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1405690178

    Chicago Manual of Style (17th edition)

osu1405690178
1,312
© 2014, some rights reserved.Creative Commons License Approximate Message Passing Algorithms for Generalized Bilinear Inference by Jason Terry Parker is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.