# Dual Decomposition Inference as long as Graphical Models over Strings Nanyun (Violet) P

## Dual Decomposition Inference as long as Graphical Models over Strings Nanyun (Violet) P

Oh, Eunice, Contributor has reference to this Academic Journal, PHwiki organized this Journal Dual Decomposition Inference as long as Graphical Models over Strings Nanyun (Violet) PengRyan Cotterell Jason EisnerJohns Hopkins University 1Attention! Dont care about phonology Listen anyway. This is a general method as long as inferring strings from other strings (if you have a probability model). So if you havent yet observed all the words of your noisy or complex language, try it! 2A Phonological ExerciseTensesVerbs3[tk][tks][tkt]TALKTHANKHACK1P Pres. Sg.3P Pres. Sg.Past TensePast Part.[tkt][ek][eks][ekt][ekt][hæk][hæks][hækt][hækt]CRACKSLAP[kæks][kækt][slæp][slæpt]

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Matrix Completion: Collaborative FilteringMoviesUsers-37291929-36677722-24617412-79-41-52-39Matrix Completion: Collaborative Filtering2919MoviesUsers29677722617412-79-41-39 -6 -3 2[ 4 1 -5][ 7 -2 0][ 6 -2 3][-9 1 4][ 3 8 -5]5[[ 9 -2 1[[ 9 -7 2[[ 4 3 -2[[-37-36-24-52Matrix Completion: Collaborative Filtering6Prediction!59-80646-37291929-36677722-24617412-79-41-52-39 -6 -3 2[[ 9 -2 1[[ 9 -7 2[[[[[ 4 1 -5][ 7 -2 0][ 6 -2 3][-9 1 4][ 3 8 -5]MoviesUsers 4 3 -2[

Matrix Completion: Collaborative Filtering[1,-4,3][-5,2,1]-10-11Dot ProductGaussian Noise7A Phonological Exercise[tk][tks][tkt]TALKTHANKHACK1P Pres. Sg.3P Pres. Sg.Past TensePast Part.TensesVerbs[tkt][ek][eks][ekt][ekt][hæk][hæks][hækt][hækt]CRACKSLAP[kæks][kækt][slæp][slæpt]8A Phonological Exercise[tk][tks][tkt]TALKTHANKHACK1P Pres. Sg.3P Pres. Sg.Past TensePast Part.Suffixes Stems[tkt][ek][eks][ekt][ekt][hæk][hæks][hækt][hækt]CRACKSLAP[kæks][kækt][slæp][slæpt]/Ø//s//t//t//tk//ek//hæk//slæp//kæk/9

A Phonological Exercise[tk][tks][tkt]TALKTHANKHACK1P Pres. Sg.3P Pres. Sg.Past TensePast Part.[tkt][ek][eks][ekt][ekt][hæk][hæks][hækt][hækt]CRACKSLAP[kæks][kækt][slæp][slæpt]/Ø//s//t//t//tk//ek//hæk//slæp//kæk/10Suffixes StemsA Phonological Exercise[tk][tks][tkt]TALKHACK1P Pres. Sg.3P Pres. Sg.Past TensePast Part.[tkt][ek][eks][ekt][ekt][hæk][hæks][hækt][hækt]CRACKSLAP[kæk][kæks][kækt][kækt][slæp][slæps][slæpt][slæpt]/Ø//s//t//t//tk//ek//hæk//slæp//kæk/Prediction!11THANKSuffixes StemsA Model of PhonologytkstksConcatenatetalks12

A Phonological Exercise[tk][tks][tkt]TALKTHANKHACK1P Pres. Sg.3P Pres. Sg.Past TensePast Part.[tkt][ek][eks][ekt][ekt][hæk][hæks][hækt][hækt]CRACKSLAPCODEBAT[kæks][kækt][slæp][slæpt][kodz][kodt][bæt][bætt]/Ø//s//t//t//tk//ek//hæk//bæt//kod//slæp//kæk/13Suffixes StemsA Phonological Exercise[tk][tks][tkt]TALKHACK1P Pres. Sg.3P Pres. Sg.Past TensePast Part.[tkt][ek][eks][ekt][ekt][hæk][hæks][hækt][hækt]CRACKSLAPCODEBAT[kæks][kækt][slæp][slæpt][kodz][kodt][bæt][bætt]/Ø//s//t//t//tk//ek//hæk//bæt//kod//slæp//kæk/z instead of st instead of t14THANKSuffixes StemsA Phonological Exercise[tk][tks][tkt]TALKHACK1P Pres. Sg.3P Pres. Sg.Past TensePast Part.[tkt][ek][eks][ekt][ekt][hæk][hæks][hækt][hækt]CRACKSLAPCODEBATEAT[kæks][kækt][slæp][slæpt][kodz][kodt][bæt][bætt][it][et][itn]/Ø//s//t//t//tk//ek//hæk//it//bæt//kod//slæp//kæk/et instead of itt15THANKSuffixes Stems

A Model of Phonologykodskod skodzConcatenatePhonology (stochastic)codes16Modeling word as long as ms using latent underlying morphs in addition to phonology.Cotterell et. al. TACL 2015A Model of Phonologyrizaignationrizaign ationrzgnenresignationConcatenate17Phonology (stochastic)dæmnenzrizaignFragment of Our Graph as long as English181) Morphemes2) Underlying words3) Surface wordsConcatenationPhonologyresignationresigns3rd-person singular suffix: very common!

Limited to concatenation No, could extend to templatic morphology 19Outline20A motivating example: phonologyGeneral framework: graphical models over stringsInference on graphical models over strings Dual decomposition inferenceThe general ideaSubstring features in addition to active setExperiments in addition to resultsGraphical Models over StringsJoint distribution over many stringsVariablesRange over infinite set of all stringsRelations among variablesUsually specified by (multi-tape) FSTs21 A probabilistic approach to language change (Bouchard-Côté et. al. NIPS 2008) Graphical models over multiple strings. (Dreyer in addition to Eisner. EMNLP 2009) Large-scale cognate recovery (Hall in addition to Klein. EMNLP 2011)

Graphical Models over StringsStrings are the basic units in natural languages.UseOrthographic (spelling)Phonological (pronunciation)Latent (intermediate steps not observed directly)SizeMorphemes (meaningful subword units)WordsMulti-word phrases, including named entitiesURLs22What relationships could you modelspelling pronunciationword noisy word (e.g., with a typo)word related word in another language (loanwords, language evolution, cognates)singular plural ( as long as example)root wordunderlying as long as m surface as long as m23Chains of relations can be usefulMisspelling or pun = spelling pronunciation spellingCognate = word historical parent historical child24

Factor Graph as long as phonology25Contextual Stochastic Edit Process26Stochastic contextual edit distance in addition to probabilistic FSTs. (Cotterell et. al. ACL 2014)Probabilistic FSTs27Stochastic contextual edit distance in addition to probabilistic FSTs. (Cotterell et. al. ACL 2014)

rizajnzr,zgnenrizajndInference on a Factor Graph281) Morpheme URs2) Word URs3) Word SRsfoorizajnzr,zgnensrizajnddabarInference on a Factor Graph291) Morpheme URs2) Word URs3) Word SRsInference on a Factor Graph30foobar srizajnzbar foor,zgnensbar darizajnddabar1) Morpheme URs2) Word URs3) Word SRs

ConclusionA general DD algorithm as long as MAP inference on graphical models over strings.On the phonology problem, terminates in practice, guaranteeing the exact MAP solution. Improved inference as long as supervised model; improved EM training as long as unsupervised model.Try it as long as your own problems generalizing to new strings!76

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