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weighted Methods Importance 20 : - Sleep Planning Inference - PowerPoint PPT Presentation

Lecture weighted Methods Importance 20 : - Sleep Planning Inference Wake as - , Scribes Xiong yi Zhang : McInerney Jered Auto Variational Summary encoders : Use Idea neural to parameterize I netwonus : model , 2- ) (


  1. Lecture weighted Methods Importance 20 : - Sleep Planning Inference Wake as - , Scribes Xiong yi Zhang : McInerney Jered

  2. Auto Variational Summary encoders : Use Idea neural to parameterize I netwonus : model , 2- ) ( generative deep pg x a Use variational Idea inference auto encoding 3+4 : model inference to train ( ) Z Ix go , an ) that approximates the posterior pg CZIX from , ( to Idea Use K ) approximate samples go 2 : 7 the To log gradient pok ) Deff Idea Use to 5 parameterization compute : me

  3. Auto encoding Variational General Methods View : Variational Any Bound that method ' produces ; lower valid weight defines bound importance a a - ftp.#ggzixsllogwDsEtp..llogpdxYw=Pg%E7I Epa , # £1943 , Gradient Use Estimation ) s qczlx samples 2- : - ftp.#qopaxil0ologpocx.ZD ftp.#qopxxif9ologqq1zixsflegwlx,zstb ) ( Always some ) L ( O To , G) the = ) ) ( REINFORCE Tq L ( O 4) ) = , 2- aces ) ) ) ( Repwaweteiud ) L pce , [ Og log Tg ( x I 0,10 ) w = ,

  4. Auto encoding Variational General Methods View : - weighted Ulp Auto encoding & Importance auto encoders SMC : EI [ IT Replace unbiased estimator pocx ) with W = £194 - . ) ftp.#qzixsleogwDsEf..llogpdxyw=pofx.zy9ql7IX n ↳ lower Replace band Wake methods sleep ; - bound log with ) upper > , poles ^ 1- Planning Replace inference pot 7) target ! x. as ) T [ RIZ density pgcz ) with exp a

  5. Auto Importance weighted encodes - Auto Normal Use Marte Carlo reparauretevized encoder : £194 ) - - , II. leg = is ) ftp.t#pceileogwo.ak.xYywo.oi=g:YI:Y?T Antoon Replace Importance weighted weight coder wo.aceb.h.xbsxbnlln.it/sxYiii)qbih~pCE : w - K I E I Wh with weight = an average U I flog Eof log E) £ ( 99 ) I ) slog - leypfx # Egli ) Epa , - , = like , go , h ,xb ) ) leg ↳ £ Wo ,¢lEb' TLDR Move : ' = g k Sum over . inside log

  6. Auto Importance weighted encodes - Auto Replace Importance weighted weight encoder : w - K E ¥ I Wh with weight = an average U I , [ log I ) L ( 0,0 ) # Epa , = cziikix go , is E. leg ( II. ) ) PH3z.net#qf2-oCEb.h)/Xb = E [ I Note Any ] unbiased Cx ) defines estimation po : = ) ] [ leg lower bound Epa Pok a on , Ep flog pok ) ) I ) Epl log EGEE ) ) Egl by Ep L s = =

  7. Auto Importance weighted encodes - Gradient woo Gradients bound Computation IWAE of the ; normalized self estimates are importance sampling - CE !× ) ) L ( 90 ) , flog # ' EE Epa , = , punk T REINFORCE TRICK Wiley we w # pceiikgf.gg#If0o.$wgfEk For of lolol ) ) ) I Epix , = f # peeing Epix . wqY.l.IT?7.,0o.oibgw..pld.xY I = 9 I log weight of gradient Self weight normalized -

  8. Bound Minimizing Upper on Make similar by Idea to ) poczlx Cz ) go it ; , KL exclusive KL than minimizing inclusive rather - Note " 9 ) Mt Epa , # p.com/ ] : )= UH leg Klfqllp ) instead of ] ) = ftp.x.llogpocxyt#pcxilEpcaix,lley ! I log ) ] KL ( pottksllqotfks ) ) Epc ,→ I Ep Poet t = I log CA ) Making UH ) Ep smaller also 7 , Po the KL divergence reduces

  9. Bound Minimizing Upper an Make similar by Idea to ) poczlx Cz ) go it ; , KL exclusive KL than minimizing inclusive rather Epa , # p.com/bgPgIYIIT , ] UH = No dependence I parameters 4 on # peal To ,U4 , I 94171×3 ) Deploy ) # - = pg*× T Need from potfk samples ) method ) ( Monte Carlo use any can

  10. Bound Minimizing Upper on Make similar by Idea to ) poczlx Cz ) go it ; , KL exclusive KL than minimizing inclusive rather # peal To ,U4 , I 94171×3 ) Deploy ) # - = pg*× self IS Use normalized - • bgqattixs ) ) ftp.xsf#g.czxs/P:YIT Oo = , , Czbih , ×b § , Woio ? leg 991744×6 ) 4 I . Wo ,¢Czb4×b , EE , , [ " " - sleep to Sometimes wake referred reweighed as

  11. Wake Reweighed sleep - ' C x ) Sample Xb Wake pdat phase approximate and n : h b b' self pact 1×1 2- normalized importance using ~ - zb.hn qgzlxb ) sampling with proposal b , h LEE IT Epa , I log poem ) me to To ) = pocxb.tk - ¥EE§be Epcxilkllpottix - To 9ohm ) ) , lzbihlxbl ) " To , go = , ftp.cnn/logPg::ITIl/=fE4bggo,czbixbs from Xb Sleep b Sample phase pocx the 7) 7 : ~ , , ( often shipped ) gradient model compute generative and 9 - b

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