Xiong Zhang yi : McInerney Jered Auto encoding Variational - PowerPoint PPT Presentation

Lecture Estimators Doubly Re parameterized 20 : - Scribes Xiong Zhang yi : McInerney Jered

Auto encoding Variational General Methods View : - weighted Ulp Auto encoding & Importance auto encoders SMC : EI [ IT Replace unbiased estimator Cx ) with pg W = £194 ) ftp.#qczixsllogwDsEp..llogpdxiIw=Po&I9pl71X - - ) n ↳ lower Replace band Wake methods sleep : - bound log with ) upper > , poles

Gradient Variational Inference Estimation in Reinforce Style - d t ) ) go , czixsl log # Pok Z ) 2%5×3 wo.pk ICO wo.pk , of ,zs= , a ) = , ddqo 94171×3 9¢CZgk,x ! ( Ig leg & & a) ( log At tbh ) Wo # dd-plogwo.pk " ith ) Z aaczks = go - , , Normal x ) µ¢lxlt6¢X E. ) E 2-41 Re : = parameterized . ) E ) ) ddp Epee , flog Pok dido L ( O C x. to ) , woo , Wo ,¢c× = = , , ) IX ) K If duplet , eh ) = K k - I -

Gradient Variational Estimation Inference in Re wo.pk parameterized . " ) E ) ) Pok . Zak d- Epee , flog L ( O 9¢CZqk,x ( x. . to ) , ,oc× , woo , = Wo = def , ) IX ) K Idol log If , eh ) duplet Samples = are I K h=i equally weighted - Weighted ( Replace ) Importance weight with weight average pceikgllogltf.wo.acx.es Iw ) ) h Latos off # Foi = K x. Eh ) ( w go , d , Eh ) n pls 's ) Better I log wo.pk samples " " " E = - , { dot , El ) Wo C x higher h= have a , @ I weight

Gradient Variational Estimation Inference in - Weighted Importance Iw Llap ) adq = " ) ↳ d , Eh ) n pls 's ) I log wo.pk " " " E = - ha f dot El ) C x. Wo , @ ddqEpceikylle.gl#&!wo.4H&)HRepanameteniudkwo.glx.E self Approximate normalized with . y Style Wake sleep importance sampling - ) ) - dd-qUIO.to ) - da # ) 1h07 WORK 't = poczix Notre parameterized to d- log K zh ) 2-49,171×3 ( we ,qf× , Eh ) woo , x. I dot Opposite sign - 6=1 § , El ) Wo ( x ,

Aside Methods Sleep Wake . . ' 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 Reweighed etolegpocxb II. b , h lgffqwt.tw#e0qbgqo,lzb.hlxbl Epa , I log poem ) LEE To 744 = , - to Epcxilkllpottixllgottixl ) ) = - ftp.cnn/bgPg::ITII=fE4bggo,czbixbs from Xb Sleep 's Sample phase pocx ,7 ) the 7 : ~ , ( often shipped ) gradient model compute generative and 9 - b

Gradient Variational Estimation Inference in - Weighted Importance ddp-Epceikyllogltuwo.lk Iw 'd ) ) ) Llap ) ddq = Wahef Repanameteniud " ) ↳ K ( E woo , x. d Wo ,p(X , Eh ) I log Sleep E' i " phase npcglik ) = - , § dot , El ) shipped Wo ( x generally h= , i. sleep ) Style - & ftp.czixs/h0FW0HHZ ) ) - dd-qUIO.to ) = Notre parameterized to d- log K zh ) 2-49,171×3 ( we ,¢(× , Eh ) woo , x. I dot Opposite sign - 6=1 & , El ) Wo C x ,

- style Reinforce Gradient log gettin ddqLn_Iffadqlogqacz4xDflogwCx.z4tb7Zzg@logpoCx.z.s 2- , Idea . Higher towards 94171×3 move i zh sumpters have that Ip log I ) tix Higher log wo.pk 2 t ) . ,

- style Reinforce Gradient = I f ¥ ( ad-glogqaczh.la/flogwCx.z4tb7 L log Zz ④ Pok as , zh log gettin 2- , Idea . Higher towards 94171×3 move i zh sumpters have that Ip log I ) tix Higher log wo.pk 2 t ) . ,

- style Reinforce Gradient = I f ¥ ( ad-glogqaczh.la/flogwCx.z4tb7 L log Zz ④ Pok as , zh log gettin 2- , Idea . Higher towards 94171×3 move i zh sumpters have that Ip log I ) tix Higher log wo.pk 2 t ) . ,

- style Reinforce Gradient = I f ¥ ( ad-glogqaczh.IN/flogwCx.z4tb7 L log Zz ④ . > Pok ,z 9 To • zh & log gettin . 2- I Idea . Higher towards 94171×3 move i zh sumpters have that Ip log I ) tix Higher log wo.pl 2 -577 .

- style Depanaweten Gradient Reinforce Gradient iced - ¥ § ( L = log log Zz Zz § § . ) Pok pocx.rs ,z 9 To a zh • z-q.ie?x7logqqCzix7 adqlogqaczh.la/flogwCx.z4tb7ddqL--tEfddplogwo.qCx,E7 log gettin . Zi 2- , Move in direction Idea dea 94171×1 . Higher towards qolczlxs : move : zh samples have log that that will Woo , ( , E ) increase x Ip log I = ! 9ft ' " - Iglesia logwdzs 't ' " adqeogw Higher log wo.plx.es 09 2 .

- style Depanaweten Gradient Reinforce Gradient iced - ¥ § ( L = log Zz § pocx.rs Zzg@logpoCx.z.s To % . zh • z-g.ie?x7logqqCz1x7 adqlogqaczh.la/flogwCx.z4+b7ddqL--tEfddplogwo.qCx,E7 log q¢Cz1x ) . Zi 2- , Move in direction Idea dea 94171×1 . Higher towards qolczlxs : move : that log zh will samples have , E ) that increase wo.pk Ip log I = ! 9ft ' " - Iglesia logwdzs 't ' " adqeogw Higher log wo.plx.es 09 2 .

- style Depanaweten Gradient Reinforce Gradient iced - ¥ § ( L = log log Zz Zz § § . > Pok pocx.rs ,z To % . zh • adqlogqaczh.la/flogwCx.z4tb7ddqL--tEfddplogwo.qCx,E7 z-q.ie?x7logqqCzlx7 log gettin . Zi 2- , Move in direction Idea dea 94171×1 . Higher towards qolczlxs : move i zh sumpters have that that log will , E ) increase wo.pk Talos I = ! logwffq 9ft ' " - Iglesia 't ' " adqeogw Higher log wo.qlx.tt 2 ) .

Importance weighted - , Eh ) w C x § gee Fold , ddqlogwlx.ch ) = logPo"g 2- ⑥ z High weight self normalized ' = . ↳ self normalized weight yo w - # log q¢cz,× , 2- , Multiply Idea adqlogwcx.es : by self the weight normalized - , Eh ) ( - ooqeeyqa.in ) X Gwf } w , ,

Importance weighted - , Eh ) w C x ddqLi_YfqwI.egddqlogwlx.ehIZzg@logpoCx.z.s . log gettin 2- , Multiply Idea adqlogwcx.es : by self the weight normalized - , Eh ) ( - ooqeegoioieixl ) X btw :& w ee ,

Importance weighted - fqwI.ee , Eh ) dqL= w C x , dd-qlogwk.de ' Problem High weight samples * : have signal ratio low to noise - log - Zz . § Samples that to closer are " . log have higher pocx.tn a but log q¢Czix ) weight also ) wcx E , larger have , log CZKT z ddg a go , - , Multiply Idea adqlogwcx.es : by self the weight normalized - ) , Eh ) ( X btw :3 w - ooqeey9.mx , ee ,

Style Importance Wake sleep weighted - - Wh d ' - log Zz ④ Pok " , . dqdn-fq-wed-qlogwk.de www.ixi/wqIiIe,ofaees9oithw dd_pU-nfgh-eweadqloggoiCzhk7Zg@logpocx.z.s log log gettin gettin Zi Zi d Multiply Multiply af log 9171×1 Idea adqlogwcx.es Idea : : by by self the self weight weight the normalized normalized - - I how :& 2- e

Doubly Re parameterized Estimators - Effie I :* h - few ; IN ) DI = e d h Of l 0,9 King a ¥¢bg9¢GK ) Rewrite term Idea identity : logwhggiooqeeyg.a.in , I fc2.ch#logqaczix ) ] Epee , I 8¥ 8¥ ) F- - . can q¢ . ) ( for Appendix 8.1 of at proof Tincher et see h we h :& : W ) I wo.IO f 0,9 07 's 07 = - - em :p . se . . - ¥3 . . ! WO ( qw.io log who OZ , ¢ trial ) go , Reinforce ( use ,

" Intf Doubly Re parameterized Estimators - www.ixi nigh fit h IN E ) df log go = . , e d h Of l O , of King a qacziix Iq leg Rewrite 9,41×7 term Idea identity : h Escamilla ) ] Tejo # log ⇐ " a .dz , , :* :& ÷ : : eosw :* . :# I . Sau TLDR the ⇐ ( woah ) ' : are § , log who , 8¥ d£p±w= & weights the drop o ( f Yolo ' , ) , o . terms of leg go can ,

Doubly Re parameterized Estimators - ii. Doubly Reparameterized Singly Reparameteriud " " ⑧ & . . 2- I 2- , wo.0://8.eog.io ( www.ixi ⇐ how :* ) :* ) , £ Yoo , ' e s All No terms signal problems to : not mane - - 8¥ leg wgho to proportional ,

. sleep Weighting Wake Combining Importance and . ddgth - a) AFL U bound Tane combination Idea of upper convex : L bound lower and d d og 'll I I a - = If doubly parameterized Use re - both estimator for bounds K =L ftp.etci-zas/gwo:.l)f9.eoswho..:Ei ) be - , - Reweighed - sleep Importune wake weighted D= STL 0.5 0=1 9=0 - -