000203543 001__ 203543
000203543 005__ 20181203023709.0
000203543 0247_ $$2doi$$a10.1109/TSP.2014.2357776
000203543 022__ $$a1053-587X
000203543 02470 $$2ISI$$a000344466200004
000203543 037__ $$aARTICLE
000203543 245__ $$aBilinear Generalized Approximate Message Passing—Part I: Derivation
000203543 269__ $$a2014
000203543 260__ $$aPiscataway$$bInstitute of Electrical and Electronics Engineers$$c2014
000203543 300__ $$a15
000203543 336__ $$aJournal Articles
000203543 520__ $$aIn this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its application to matrix completion, robust PCA, dictionary learning, and related matrix-factorization problems. Here, in Part I of a two-part paper, we derive our Bilinear G-AMP (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. In Part II of the paper, we will discuss the specializations of EM-BiG-AMP to the problems of matrix completion, robust PCA, and dictionary learning, and we will present the results of an extensive empirical study comparing EM-BiG-AMP to state-of-the-art algorithms on each problem.
000203543 6531_ $$aApproximate message passing
000203543 6531_ $$abelief propagation
000203543 6531_ $$abilinear estimation
000203543 6531_ $$amatrix completion
000203543 6531_ $$adictionary learning
000203543 6531_ $$arobust principal components analysis
000203543 6531_ $$amatrix factorization
000203543 700__ $$aParker, J.T.
000203543 700__ $$aSchniter, P.
000203543 700__ $$0243957$$aCevher, Volkan$$g199128
000203543 773__ $$j62$$k22$$q5839 - 5853$$tIEEE Transactions on Signal Processing
000203543 8564_ $$s5841873$$uhttps://infoscience.epfl.ch/record/203543/files/06898015.pdf$$yn/a$$zn/a
000203543 909C0 $$0252306$$pLIONS$$xU12179
000203543 909CO $$ooai:infoscience.tind.io:203543$$pSTI$$particle$$qGLOBAL_SET
000203543 917Z8 $$x231598
000203543 937__ $$aEPFL-ARTICLE-203543
000203543 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000203543 980__ $$aARTICLE