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Morphology & FSTs Shallow Processing Techniques for NLP Ling570 October 17, 2011

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Roadmap Two-level morphology summary Unsupervised morphology

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Combining FST Lexicon & Rules Two-level morphological system: ‘Cascade’ Transducer from Lexicon to Intermediate Rule transducers from Intermediate to Surface

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Integrating the Lexicon Replace classes with stems

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Using the E-insertion FST (fox,fox): q0, q0,q0,q1, accept (fox#,fox#): q0.q0.q0.q1,q0, accept (fox^s#,foxes#): q0,q0,q0,q1,q2,q3,q4,q0,accept (fox^s,foxs): q0,q0,q0,q1,q2,q5,reject (fox^z#,foxz#) ?

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Issues What do you think of creating all the rules for a languages – by hand? Time-consuming, complicated

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Issues What do you think of creating all the rules for a languages – by hand? Time-consuming, complicated Proposed approach: Unsupervised morphology induction

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Issues What do you think of creating all the rules for a languages – by hand? Time-consuming, complicated Proposed approach: Unsupervised morphology induction Potentially useful for many applications IR, MT

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Unsupervised Morphology Start from tokenized text (or word frequencies) talk 60 talked120 walked40 walk30

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Unsupervised Morphology Start from tokenized text (or word frequencies) talk 60 talked120 walked40 walk30 Treat as coding/compression problem Find most compact representation of lexicon Popular model MDL (Minimum Description Length) Smallest total encoding: Weighted combination of lexicon size & ‘rules’

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Approach Generate initial model: Base set of words, compute MDL length

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Approach Generate initial model: Base set of words, compute MDL length Iterate: Generate a new set of words + some model to create a smaller description size

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Approach Generate initial model: Base set of words, compute MDL length Iterate: Generate a new set of words + some model to create a smaller description size E.g. for talk, talked, walk, walked 4 words

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Approach Generate initial model: Base set of words, compute MDL length Iterate: Generate a new set of words + some model to create a smaller description size E.g. for talk, talked, walk, walked 4 words 2 words (talk, walk) + 1 affix (-ed) + combination info 2 words (t,w) + 2 affixes (alk,-ed) + combination info

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Successful Applications Inducing word classes (e.g. N,V) by affix patterns Unsupervised morphological analysis for MT Word segmentation in CJK Word text/sound segmentation in English

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Unit #1 Summary

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Formal Languages Formal Languages and Grammars Chomsky hierarchy Languages and the grammars that accept/generate

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Formal Languages Formal Languages and Grammars Chomsky hierarchy Languages and the grammars that accept/generate Equivalences Regular languages Regular grammars Regular expressions Finite State Automata

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Finite-State Automata & Transducers Finite-State Automata: Deterministic & non-deterministic automata Equivalence and conversion Probabilistic & weighted FSAs

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Finite-State Automata & Transducers Finite-State Automata: Deterministic & non-deterministic automata Equivalence and conversion Probabilistic & weighted FSAs Packages and operations: Carmel

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Finite-State Automata & Transducers Finite-State Automata: Deterministic & non-deterministic automata Equivalence and conversion Probabilistic & weighted FSAs Packages and operations: Carmel FSTs & regular relations Closures and equivalences Composition, inversion

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FSA/FST Applications Range of applications: Parsing Translation Tokenization…

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FSA/FST Applications Range of applications: Parsing Translation Tokenization… Morphology: Lexicon: cat: N, +Sg; -s: Pl Morphotactics: N+PL Orthographic rules: fox + s foxes Parsing & Generation

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Implementation Tokenizers FSA acceptors FST acceptors/translators Orthographic rule as FST

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Language Modeling

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Roadmap Motivation: LM applications N-grams Training and Testing Evaluation: Perplexity

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Predicting Words Given a sequence of words, the next word is (somewhat) predictable: I’d like to place a collect …..

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Predicting Words Given a sequence of words, the next word is (somewhat) predictable: I’d like to place a collect ….. Ngram models: Predict next word given previous N Language models (LMs): Statistical models of word sequences

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Predicting Words Given a sequence of words, the next word is (somewhat) predictable: I’d like to place a collect ….. Ngram models: Predict next word given previous N Language models (LMs): Statistical models of word sequences Approach: Build model of word sequences from corpus Given alternative sequences, select the most probable

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N-gram LM Applications Used in Speech recognition Spelling correction Augmentative communication Part-of-speech tagging Machine translation Information retrieval

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Terminology Corpus (pl. corpora): Online collection of text of speech E.g. Brown corpus: 1M word, balanced text collection E.g. Switchboard: 240 hrs of speech; ~3M words

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Terminology Corpus (pl. corpora): Online collection of text of speech E.g. Brown corpus: 1M word, balanced text collection E.g. Switchboard: 240 hrs of speech; ~3M words Wordform: Full inflected or derived form of word: cats, glottalized

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Terminology Corpus (pl. corpora): Online collection of text of speech E.g. Brown corpus: 1M word, balanced text collection E.g. Switchboard: 240 hrs of speech; ~3M words Wordform: Full inflected or derived form of word: cats, glottalized Word types: # of distinct words in corpus

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Terminology Corpus (pl. corpora): Online collection of text of speech E.g. Brown corpus: 1M word, balanced text collection E.g. Switchboard: 240 hrs of speech; ~3M words Wordform: Full inflected or derived form of word: cats, glottalized Word types: # of distinct words in corpus Word tokens: total # of words in corpus

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Corpus Counts Estimate probabilities by counts in large collections of text/speech Should we count: Wordform vs lemma ? Case? Punctuation? Disfluency? Type vs Token ?

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Words, Counts and Prediction They picnicked by the pool, then lay back on the grass and looked at the stars.

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Words, Counts and Prediction They picnicked by the pool, then lay back on the grass and looked at the stars. Word types (excluding punct):

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Words, Counts and Prediction They picnicked by the pool, then lay back on the grass and looked at the stars. Word types (excluding punct): 14 Word tokens (“ ):

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Words, Counts and Prediction They picnicked by the pool, then lay back on the grass and looked at the stars. Word types (excluding punct): 14 Word tokens (“ ): 16. I do uh main- mainly business data processing Utterance (spoken “sentence” equivalent)

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Words, Counts and Prediction They picnicked by the pool, then lay back on the grass and looked at the stars. Word types (excluding punct): 14 Word tokens (“ ): 16. I do uh main- mainly business data processing Utterance (spoken “sentence” equivalent) What about: Disfluencies main-: fragment uh: filler (aka filled pause)

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Words, Counts and Prediction They picnicked by the pool, then lay back on the grass and looked at the stars. Word types (excluding punct): 14 Word tokens (“ ): 16. I do uh main- mainly business data processing Utterance (spoken “sentence” equivalent) What about: Disfluencies main-: fragment uh: filler (aka filled pause) Keep, depending on app.: can help prediction; uh vs um

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LM Task Training: Given a corpus of text, learn probabilities of word sequences

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LM Task Training: Given a corpus of text, learn probabilities of word sequences Testing: Given trained LM and new text, determine sequence probabilities, or Select most probable sequence among alternatives

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LM Task Training: Given a corpus of text, learn probabilities of word sequences Testing: Given trained LM and new text, determine sequence probabilities, or Select most probable sequence among alternatives LM types: Basic, Class-based, Structured

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Word Prediction Goal: Given some history, what is probability of some next word? Formally, P(w|h) e.g. P(call|I’d like to place a collect)

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Word Prediction Goal: Given some history, what is probability of some next word? Formally, P(w|h) e.g. P(call|I’d like to place a collect) How can we compute?

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Word Prediction Goal: Given some history, what is probability of some next word? Formally, P(w|h) e.g. P(call|I’d like to place a collect) How can we compute? Relative frequency in a corpus C(I’d like to place a collect call)/C(I’d like to place a collect) Issues?

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Word Prediction Goal: Given some history, what is probability of some next word? Formally, P(w|h) e.g. P(call|I’d like to place a collect) How can we compute? Relative frequency in a corpus C(I’d like to place a collect call)/C(I’d like to place a collect) Issues? Zero counts: language is productive! Joint word sequence probability of length N: Count of all sequences of length N & count of that sequence

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Word Sequence Probability Notation: P(X i =the) written as P(the) P(w 1 w 2 w 3 …w n ) =

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Word Sequence Probability Notation: P(X i =the) written as P(the) P(w 1 w 2 w 3 …w n ) = Compute probability of word sequence by chain rule Links to word prediction by history

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Word Sequence Probability Notation: P(X i =the) written as P(the) P(w 1 w 2 w 3 …w n ) = Compute probability of word sequence by chain rule Links to word prediction by history Issues?

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Word Sequence Probability Notation: P(X i =the) written as P(the) P(w 1 w 2 w 3 …w n ) = Compute probability of word sequence by chain rule Links to word prediction by history Issues? Potentially infinite history

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Word Sequence Probability Notation: P(X i =the) written as P(the) P(w 1 w 2 w 3 …w n ) = Compute probability of word sequence by chain rule Links to word prediction by history Issues? Potentially infinite history Language infinitely productive

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Markov Assumptions Exact computation requires too much data

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Markov Assumptions Exact computation requires too much data Approximate probability given all prior words Assume finite history

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Markov Assumptions Exact computation requires too much data Approximate probability given all prior words Assume finite history Unigram: Probability of word in isolation (0 th order) Bigram: Probability of word given 1 previous First-order Markov Trigram: Probability of word given 2 previous

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Markov Assumptions Exact computation requires too much data Approximate probability given all prior words Assume finite history Unigram: Probability of word in isolation (0 th order) Bigram: Probability of word given 1 previous First-order Markov Trigram: Probability of word given 2 previous N-gram approximation Bigram sequence

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Unigram Models P(w 1 w 2 …w 3 )~

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Unigram Models P(w 1 w 2 …w 3 ) ~ P(w 1 )*P(w 2 )*…*P(w n ) Training: Estimate P(w) given corpus

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Unigram Models P(w 1 w 2 …w 3 ) ~ P(w 1 )*P(w 2 )*…*P(w n ) Training: Estimate P(w) given corpus Relative frequency:

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Unigram Models P(w 1 w 2 …w 3 ) ~ P(w 1 )*P(w 2 )*…*P(w n ) Training: Estimate P(w) given corpus Relative frequency: P(w) = C(w)/N, N=# tokens in corpus How many parameters?

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Unigram Models P(w 1 w 2 …w 3 ) ~ P(w 1 )*P(w 2 )*…*P(w n ) Training: Estimate P(w) given corpus Relative frequency: P(w) = C(w)/N, N=# tokens in corpus How many parameters? Testing: For sentence s, compute P(s) Model with PFA: Input symbols? Probabilities on arcs? States?

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Bigram Models P(w 1 w 2 …w 3 ) = P(BOS w 1 w 2 ….w n EOS)

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Bigram Models P(w 1 w 2 …w 3 ) = P(BOS w 1 w 2 ….w n EOS) ~ P(BOS)*P(w 1 |BOS)*P(w 2 |w 1 )*…*P(w n |w n-1 )*P(EOS|w n ) Training: Relative frequency:

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Bigram Models P(w 1 w 2 …w 3 ) = P(BOS w 1 w 2 ….w n EOS) ~ P(BOS)*P(w 1 |BOS)*P(w 2 |w 1 )*…*P(w n |w n-1 )*P(EOS|w n ) Training: Relative frequency: P(w i |w i-1 ) = C(w i-1 w i )/C(w i-1 ) How many parameters?

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Bigram Models P(w 1 w 2 …w 3 ) = P(BOS w 1 w 2 ….w n EOS) ~ P(BOS)*P(w 1 |BOS)*P(w 2 |w 1 )*…*P(w n |w n-1 )*P(EOS|w n ) Training: Relative frequency: P(w i |w i-1 ) = C(w i-1 w i )/C(w i-1 ) How many parameters? Testing: For sentence s, compute P(s) Model with PFA: Input symbols? Probabilities on arcs? States?

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Trigram Models P(w 1 w 2 …w 3 ) = P(BOS w 1 w 2 ….w n EOS)

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Trigram Models P(w 1 w 2 …w 3 ) = P(BOS w 1 w 2 ….w n EOS) ~ P(BOS)*P(w 1 |BOS)*P(w 2 |BOS,w 1 )*… *P(w n |w n-2, w n- 1 )*P(EOS|w n-1, w n ) Training: P(w i |w i-2,w i-1 )

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Trigram Models P(w 1 w 2 …w 3 ) = P(BOS w 1 w 2 ….w n EOS) ~ P(BOS)*P(w 1 |BOS)*P(w 2 |BOS,w 1 )*… *P(w n |w n-2, w n- 1 )*P(EOS|w n-1, w n ) Training: P(w i |w i-2,w i-1 ) = C(w i-2 w i-1 w i )/C(w i-2 w i-1 ) How many parameters?

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Trigram Models P(w 1 w 2 …w 3 ) = P(BOS w 1 w 2 ….w n EOS) ~ P(BOS)*P(w 1 |BOS)*P(w 2 |BOS,w 1 )*… *P(w n |w n-2, w n- 1 )*P(EOS|w n-1, w n ) Training: P(w i |w i-2,w i-1 ) = C(w i-2 w i-1 w i )/C(w i-2 w i-1 ) How many parameters? How many states?

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Speech and Language Processing - Jurafsky and Martin An Example I am Sam Sam I am I do not like green eggs and ham

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Recap Ngrams: # FSA states:

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Recap Ngrams: # FSA states: |V| n-1 # Model parameters:

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Recap Ngrams: # FSA states: |V| n-1 # Model parameters: |V| n Issues:

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Recap Ngrams: # FSA states: |V| n-1 # Model parameters: |V| n Issues: Data sparseness, Out-of-vocabulary elements (OOV) Smoothing Mismatches between training & test data Other Language Models

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