Day 2: Pruning continued; begin competition models

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Day 2: Pruning continued; begin competition models. Roger Levy University of Edinburgh &amp; 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

Today
• Concept from probability theory: marginalization
• Complete Jurafsky 1996: modeling online data
• Begin competition models
Marginalization
• 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
Today
• Concept from probability theory: marginalization
• Complete Jurafsky 1996: modeling online data
• Begin competition models
Modeling online parsing
• 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

Limited parallel parsing
• 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

Modeling online parsing: garden paths
• 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)
Garden path models 1: N/V ambiguity
• 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

N/V ambiguity (2)
• 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
N/V ambiguity (3)
• 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

(that was)

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

Garden path models II (2)
• 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

Notes on the probabilistic model
• 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

sometimes approximated as

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
Jurafsky 1996 & pruning: main points
• 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
General issues
• 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?
Today
• Concept from probability theory: marginalization
• Complete Jurafsky 1996: modeling online data
• Begin competition models
General idea
• 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
Origins of competition models
• 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
Origins of competition models (2)
• 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
Origins of competition models (3)
• 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)

Competition in syntactic processing
• 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]
Constraint types
• 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