稀疏贝叶斯学习(Sparse Bayesian Learning) - UCSD DSP LAB

1 (Sparse Bayesian learning ) Zhilin Zhang Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA 92093-0407, USA 1 Sparse Bayesian learning , SBL Tipping 2001 [Tipping2001] / [Wipf2004,Ji2008] Wipf Rao SBL L1 Lasso Basis Pursuit L1 SBL [Donoho2003] L1 global minimum Wipf2004] SBL sensing matrix L1 L1 Approximate Message Passing Matching Pursuit SBL Wipf_NIPS2011] SBL SBL L1 iterative reweighted L1 minimization L1 [Wipf2010] Candes L1 [Candes2008] SBL [ModelCS] SBL SBL Zhang Rao (Block Sparse Bayesian learning , BSBL)[Zhang_IEEE2011, Zhang_TSP2012] spatial structure temporal structure multi-task learning [Wan2012] [Zhang_TBME2012a, Zhang_TBME2012b] [Zhang_PIEEE2012] SBL BSBL 2.

2 VAxy+= 1 N M N 1 M SBL Ayxvxxi [Wipf2004] MiNxpiii,,1),,0();("== 2 1 i ixxi automatic relevance [ARD1996] i SBL i 0=i ixi i SBL SBL v),,0();(Iv Np= ( {} ,1 Mii=) x (Maximum A Posterior) (Type II Maximum Likelihood) [Tipping2001, MacKay1992] SBL i i non-informative prior Wipf Rao SBL [Wipf2004] i non-informative prior [Wipf_PhDThesis] Tipping SBL [Tipping2001] precision Gamma prior improper prior ixixiixxp1)

3 ( prior Laplace prior Wipf Rao SBL Tipping SBL SBL improper prior SBL Tipping,Wipf SBL SBL precision Laplace prior[BCSlaplace] SBL (sensing matrix) SBL ixixixx x Zhang Rao Zhang_IEEE2011 SBL 2.)

4 Block structure group structure groupLasso, ModelCS, Eldar2010 BSS x 3 TdddTgggTxxxx],,,,,,[11111 "" "xxx+ = (1)(3) Block Sparse Model x g x Group Lasso [groupLasso], Block-OMP [Eldar2010 BSS], Block-CoSaMP [ModelCS] (Intra-Block Correlation) Zhang Rao Block Sparse Bayesian learning , BSBL [Zhang_TSP2012] Zhang_TBME2012a, Zhang_TBME2012b BSBL ix),()(iiiNpB0x = 3 iBi SBL 00=i 0x=i prior Automatic Relevance Prior automatic relevance determination(ARD) i (Block Sparsity) ),().

5 (I0v Np= x x Zhang Rao Zhang_IEEE2011 BSBL regularize overfitting Zhang_IEEE2011, Zhang_TSP2012, Zhang_ICASSP2012 B Zhang_TSP2012 B iBiBiBiBiBIBB + Zhang_IEEE2011 3 BSBL Zhang_TSP2012, RaoZhangJin2012 Group Lasso iBiB Zhang_TSP2012 Zhang Rao BSBL Group Lasso Zhang Rao BSBL cost function = ++ =giiiTikikw11)(22)

6 1(minargxBxAxyxx k Group Lasso iwiBiw =giqpi1x Zhang_ICML2011 Group Lasso 1,2==qp Zhang_ICASSP2011 L2 BSBL Group Lasso Group Lasso BSBL 2,2==qp [Zhang_ICASSP2012, Zhang_TSP2012] BSBL BSBL BSBL (regularization parameter) BSBL BSBL Zhang_TBME2012a, Zhang_TBME2012b BSBL.)

7 1t2tLt )()()(111tttvAxy+= .. )()()(222tttvAxy+=)()()(LLLtttvAxy+= L A)(ntxLn,,1"= 4 VAXY+= )](,),([1 LttyyY"= )](,),([1 LttxxX"= Multiple Measurement Vector Model, MMV Cotter2005 L MMV RaoZhangJin2012,Cotter2005, Eldar2010, Tang2011 X)(ntx MMV MMV SBL Wipf2007 Zhang_IEEE2011 Zhang Rao MMV BSBL MMV BSBL SBL Zhang_IEEE2011 SBL MMV XiB MMV multi-task learning [Wan2012] SBL adaptive kernels.

8 3 - BSBL BSBL [RaoZhangJin2012] 4 Wireless Body-Area Network, WBAN [Mamaghanian2011, Dixon_BME2012, Eduardo2010] 1 0 1 binary sparse matrix [Mamaghanian2011] [Milenkovic2006, Calhoun2012] 2 Zhang_TBME2012a compressive 5 Makeig1996 Zhang_TBME2012b BSBL

9 BSBL Zhang_TBME2012a, Zhang_TBME2012b BSBL BSBL BSBL-BO Zhang_TSP2012 1(a) sista/daisy QRS 80 200 QRS x 125x250 binary 15 0 AAxAAxy= y BSBL-BO y x 1(b) QRS 1(c) BSBL-BO QRS A BSBL-BO 10 25 x 1(a) BSBL (regularization) Zhang_TBME2012a, Zhang_TSP2012, Zhang_ICASSP2012 x CoSaMP [Needell2009] Elastic Net [Zou2005] SL0 [Mohimani2009] Block-OMP [Eldar2010 BSS] StructOMP [Huang2009] BM-MAP-OMP [Faktor2012]

10 Zhang_TBME2012a 2 QRS BSBL BSBL BSBL Zhang_TBME2012a, Zhang_TBME2012b BSBL-BO BSBL-BO BSBL-BO BSBL fetal ECG signal(a) exploiting intra-block correlation(b) igorning intra-block correlation(c) 1. BSBL-BO (b) BSBL-BO (c) 2.