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# Day 2: Pruning continued; begin competition models - PowerPoint PPT Presentation

Day 2: Pruning continued; begin competition models. Roger Levy University of Edinburgh & University of California – San Diego. Today. Concept from probability theory: marginalization Complete Jurafsky 1996: modeling online data Begin competition models. Marginalization.

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### Day 2: Pruning continued;begin competition models

Roger Levy

University of Edinburgh

&

University of California – San Diego

• Concept from probability theory: marginalization

• Complete Jurafsky 1996: modeling online data

• Begin competition models

• In many cases, a joint p.d. will be more “basic” than the raw distribution of any member variable

• Imagine two dice with a weak spring attached

• No independence → joint more basic

• The resulting distribution over Y is known as the marginal distribution

• Calculating P(Y) is called marginalizing over X

• Concept from probability theory: marginalization

• Complete Jurafsky 1996: modeling online data

• Begin competition models

• Does this sentence make sense?

The complex houses married and single students and their families.

The warehouse fires a dozen employees each year.

• And this one?

The warehouse fires destroyed all the buildings.

• fires can be either a noun or a verb. So can houses:

[NP The complex] [VP houses married and single students…].

• These are garden path sentences

• Originally taken as some of the strongest evidence for serial processing by the human parser

Frazier and Rayner 1987

• Full-serial: keep only one incremental interpretation

• Full-parallel: keep all incremental interpretations

• Limited parallel: keep some but not all interpretations

• In a limited parallel model, garden-path effects can arise from the discarding of a needed interpretation

[S [NP The complex] [VP houses…] …]

[S [NP The complex houses …] …]

kept

• Pruning strategy for limited ranked-parallel processing

• Each incremental analysis is ranked

• Analyses falling below a threshold are discarded

• In this framework, a model must characterize

• The incremental analyses

• The threshold for pruning

• Jurafsky 1996: partial context-free parses as analyses

• Probability ratio as pruning threshold

• Ratio defined as P(I) : P(Ibest)

• (Gibson 1991: complexity ratio for pruning threshold)

• Each analysis is a partial PCFG tree

• Tree prefix probability used for ranking of analysis

• Partial rule probs marginalize over rule completions

these nodes are actually

still undergoing expansion

*implications for granularity of structural analysis

• Partial CF tree analysis of the complex houses…

• Analysis of houses as noun has much lower probability than analysis as verb (> 250:1)

• Hypothesis: the low-ranking alternative is discarded

• Note that top-down vs. bottom-up questions are immediately implicated, in theory

• Jurafsky includes the cost of generating the initial NP under the S

• of course, it’s a small cost as P(S -> NP …) = 0.92

• If parsing were bottom-up, that cost would not have been explicitly calculated yet

Garden path models II

• The most famous garden-paths: reduced relative clauses (RRCs) versus main clauses (MCs)

• From the valence + simple-constituency perspective, MC and RRC analyses differ in two places:

The horse raced past the barn fell.

p=0.14

p≈1

best intransitive:

p=0.92

transitive valence: p=0.08

• 82 : 1 probability ratio means that lower-probability analysis is discarded

• In contrast, some RRCs do not induce garden paths:

• Here, found is preferentially transitive (0.62)

• As a result, the probability ratio is much closer (≈ 4 : 1)

• Conclusion within pruning theory: beam threshold is between 4 : 1 and 82 : 1

• (granularity issue: when exactly does probability cost of valence get paid??? c.f. the complex houses)

The bird found in the room died.

*note also that Jurafsky does not treat found as having POS ambiguity

• Jurafsky 1996 is a product-of-experts (PoE) model

• Expert 1: the constituency model

• Expert 2: the valence model

• PoEs are flexible and easy to define, but…

• The Jurafsky 1996 model is actually deficient (loses probability mass), due to relative frequency estimation

Notes on the probabilistic model (2)

• Jurafsky 1996 predated most work on lexicalized parsers (Collins 1999, Charniak 1997)

• In a generative lexicalized parser, valence and constituency are often combined through decomposition & Markov assumptions, e.g.,

• The use of decomposition makes it easy to learn non-deficient models

• Syntactic comprehension is probabilistic

• Offline preferences explained by syntactic + valence probabilities

• Online garden-path results explained by same model, when beam search/pruning is assumed

• What is the granularity of incremental analysis?

• In [NPthe complex houses], complex could be an adjective (=the houses are complex)

• complex could also be a noun (=the houses of the complex)

• Should these be distinguished, or combined?

• When does valence probability cost get paid?

• What is the criterion for abandoning an analysis?

• Should the number of maintained analyses affect processing difficulty as well?

• Concept from probability theory: marginalization

• Complete Jurafsky 1996: modeling online data

• Begin competition models

• Disambiguation: when different syntactic alternatives are available for a given partial input, each alternative receives support from multiple probabilistic information sources

• Competition: the different alternatives compete with each other until one wins, and the duration of competition determines processing difficulty

• Parallel competition models of syntactic processing have their roots in lexical access research

• Initial question: process of word recognition

• are all meanings of a word simultaneously accessed?

• or are only some (or one) meanings accessed?

• Parallel vs. serial question, for lexical access

• Testing access models: priming studies show that subordinate (= less frequent) meanings are accessed as well as dominant (=more frequent) meanings

• Also, lexical decision studies show that more frequent meanings are accessed more quickly

• Lexical ambiguity in reading: does the amount of time spent on a word reflect its degree of ambiguity?

• Readers spend more time reading equibiased ambiguous words than non-equibiased ambiguous words (eye-tracking studies)

• Different meanings compete with each other

Of course the pitcher was often forgotten…

?

?

Rayner and Duffy (1986); Duffy, Morris, and Rayner (1988)

• Can this idea of competition be applied to online syntactic comprehension?

• If so, then multiple interpretations of a partial input should compete with one another and slow down reading

• does this mean increase difficulty of comprehension?

• [compare with other types of difficulty, e.g., memory overload]

• Configurational bias: MV vs. RR

• Thematic fit (initial NP to verb’s roles)

• i.e., Plaus(verb,noun), ranging from

• Bias of verb: simple past vs. past participle

• i.e., P(past | verb)*

• Support of by

• i.e., P(MV | <verb,by>) [not conditioned on specific verb]

• That these factors can affect processing in the MV/RR ambiguity is motivated by a variety of previous studies (MacDonald et al. 1993, Burgess et al. 1993, Trueswell et al. 1994 (c.f. Ferreira & Clifton 1986), Trueswell 1996)

*technically not calculated this way, but this would be the rational reconstruction