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Ifip fu ptpensdx HUAI Dcp 1105 Here VCH fflnryskcx.yst - PDF document

Kernetroed Stem Discrepancy Descent Stern Variational Gradient for Ecp Sph Cfp Dx Doe 27th tell Vibe tf Reus V CPS 154 e U minimizes FptpYD sef dncp.lk vs c For such E Ifip fu ptpensdx HUAI Dcp 1105 Here VCH fflnryskcx.yst


  1. Kernetroed Stem Discrepancy Descent Stern Variational Gradient for Ecp Sph Cfp Dx Doe 27th tell Vibe tf Reus V CPS 154 e U minimizes FptpYD sef dncp.lk vs c For such E Ifip fu ptpensdx HUAI Dcp 1105 Here VCH fflnryskcx.yst vykcx.ysdpcysdcpnrk A qfff.TT best Epl ref's 11811ns

  2. t T ol 71nr.cf ftp.i Ki Stah Discrepancy Goodness of fit Tests for KSD A ICML 16 Lee Jordan Liu Coodness of Test fit how well do the observed Measurdy the fitted model to data correspond Ho V M V µ an Hi Min i U known Xiu Xu pl

  3. Two sample test i 4 mom likelihood based approaches CDF Need to compete likelihoods generative models X hidden variable models variational methods L MCMC estimate hard to error large Curse of dimensionality Kolmogorov Xf methods Smirnov etc Traditional KSD Today Evaluating likelihood free A approach

  4. stated significance with guaranteed definition of KSD Preliminaries i KSD Properties of ii Onighd SWD approach Iii Civ Open problems i s method C 1970 s Stem's distributional for approximation metrics MMD probability sina.ge fhdm fhdvt duqu.is Moh enough Hi farmty Test function

  5. LE Lg saz Lip E Bord A DT V d K dw Gruen XIII independent variables Q or D dsel fnzxi.NL How to bound important avg rate CLT Replace the charatenisth Math idea n typically used to show cvg in f 11 11 distribution wth characterrolyoperator a by CCR Dehhe A CCR xp f A f then be the cdf of Nc orb Lee I Iq a ng ILD xf fx solves f 7

  6. result V fraedx.GR CODE for lemma Seem A Neo 1 W r v E Aflw a c f wth Elp C WH N tf W A For Cor 2 r r WfxlWDl Elf'xcw Echl I PCW x dk Generalseagidae qu.ge fhdpe fhdnI Cnn let fh solves For ghen heh where Ich how flew whew zu Nco 1 Echl 2 D for El h qq.ge EfkcwI wfhcwy Then dad pent

  7. for wadge Stern's Normal Approximation and restrict our discuss we solve Once Ron E FZ Kf Has 2 Hf'll If I on F 11 we have duc WIE EFFIE flew W few f Xi in Cor 2 for O mean independent we have Exist W nz 2 L lxiptTEFEX.ie dwcw.zje N Ross Generating a What if approximately are we with smooth density Probability distribution x by eye Replace q

  8. E Phd 2 smooth densities On X are identical g q EpCSqcxsfcxse0xfcxD EptAqtfD O.H is the Tx Ingen Sg are score function Steth is called the linear operator A q the acts on Stern's operator e f C C'CX Stem class of q i Tx fax pox Ddx Tx FIL Agf epded Efi For f

  9. Mackey 15 Gorham gy.ffEHA e.SE Sepp doffrade variational optimization a or requires So RK.MS Settings Hnk Il Hd Jex valued functions vector for RKHS strictly p d k is Ltu Lee Jordan Then in C PC Rfd For p f Definition Sep g Ks Pfp q

  10. Exxinglese spfcxskcx.x.sc Se Spex's w f r Score difference gd C ICH RSD g 97 0 g Sp p g q Characterfzadond properties ii Them 3.61 Ex a pcuecx.io'D Scp g Sgcx5kcxx Sew t with kernel ugxix sqcxJFxikcxixbe yxkexix5sqcx.lt ere Then kex xD r e Not symmetric Cp g w Red later MMD kernel A special Eglise sp 15 Notice EpcAet Proof 1 Ep Cee SHH e EplerCAet i

  11. have cfxetx y.me kex Apply it on e Sphinx's scp.gs Earing Apply it again for fixed x pg Them 3 81 EKAqkx.cm For Pan's 2 2 Scg Hpged ymeagedEpercAqfD Hyundai Proof 2 sgcxDTkcx.xblsqcxg Faxing Usg Scg g sgcxDEE.mil xs fgcxYkkcxi3 kc x's c CExksi sobkca.D.Ex.kc.MG'D

  12. above same TACK n piked as White kex Dae A Cfi Ea tip zed kcxistqkcxi.DZ Cf Eagle y Emp sqkxkfi.kcxisbe cfr.tqkcxi.be Ox kex Doe of Oxfam Cfc ExngESq4xHvxst7xifvxD Eg rLAqtD.w flushes the proof D trek

  13. to give situation in We are a estimation of Sep g an U statistics Thru 3 6 From Uecxing Qc pig Ej be used in application cBeoIgtrapg can with The connection MMD Fisher divergence Epl Sp Sel Fisher ftp.qi 1 kerndraed Fisher divergence is K S D a k.xIFcpe ifeng.FI etqscp.pe

  14. Hsg Splbe f Eg ercaqtif E.pk se Spi't for Nfl bed El Kemelbed version MMD 2 Hf bee 13 Efef Egf Egf kcxixsekcy.ys zkcx.gs Ex Cureton 10 E y y the Notice that e 0 Ey y ng Ust Y Y'I 2UqCx y is Thus RSD stem from identity asymmetric kernel Uq a MMD wth test 2 sample MMD Goodness of FM test KSD

  15. Some results asymptotic A normal For ptg asymtotically d Nco of Icp q Jn Scp q1 Emp Ugc Xi X 0 where tu Vern oof o For f q d insipid 95955 i a Gaussian edgen All standard results V of stat Me

  16. A Universal Approximation Thm Luk Lu of DNN for expressing distributions 2020 MMDCp.at Eggs I Ept Eat 1 O Tha f F f KSDlp.ak fffg.ge Ep O Thru 4 i EE Sa Then there R na Xi realizations of Pn fo Monty sie exBfs Arequelites hold for Nefstadt i Cq D W Cpn a d E 2 Cigs n ta d 3 c for pd bounded k pumpkin 1 me

  17. for k Las bdd derivatives L Lip wth Thia sub Gaussian smooth a C Fdn E KS DC Pn a understand above results Or you as can holds for as C least I S with prob at independent of n Proof Well known Sketch of 2 127 l a the llfkcxisd.tk K MMD Pma Here Sriperumbudur if X ie Xn surve ya or Y satisfies 14C Xin Xi Xn xD YC x Xi sMk Then from 2nT e with prob I e McDiarmid's Ineq Hoeffdly type H f ke E x dik t a Hae

  18. By standard symmetrization argument ZEEH TEeikc.ms be EH fkiixsdfn astbe Xi GB t 1 Ci i id Rademacher averages RHS Use McDiarmid again E Ee Henze ke iXiH µ F a mix is the Fits Eek e pg KSDTPn.at Sketch xj7 3 nEjuacxi I Use Bernstein type Meg symmetric kernel statistics for V the Ua satisfies check this kernel conditions of CThm C D degenerate Ikalx.gs Egcxsgcy7iEfgcxa4es2Jk ki 2 a C exp f GEE pl l KS Dist D

  19. A 4 e Liu Original SVC D Wang iii NeurIPs t 6 Variational Inference Problem ang mish E K L Camp Find q a simpler distribution Ee Set Tex be the density of z qq.CZ I Dee Fettes 1 gifted qq.gl Z methods consider T with certain Previous then parametric form offshore parameters that if In Efhm 3 t they noticed applying gradient descent to solve Directly q Eep dehked above For X above problem t Eder joy ddt Kneer HD CH E o TITLE ful Oe e Enna dx

  20. f areas a in were able to minimizeCH Agarh they the dhectron of steepest descent Hotbeds p E yuglkcx.yoylnfytoykcx.gs is VCD for gratzekkfe Hp this i e v Zege 4 later be discussed metric Wu will The Seen Advantages so'D C 17 Geometric structure Worry i On the geometry of SVED if I Duncan etat we need Under which condition consider this gradient flow use or to

  21. What Stem distance between measures benefit from monty portholes can we smoothly we find alternate Can some to improve SVAD apostate flows outliers rate wire i Cvg Understand the bias and variance with combine it SV GD particles or of E from the 17 I MC traditional Fundamentals of Nathan Ross And Scali

  22. Steele's method distr Approximation of Borisov I with of store V multidimensional kernels Thank you

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