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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.

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day 2 pruning continued begin competition models

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
modeling online parsing
Modeling online parsing
  • Does this sentence make sense?

The complex houses married and single students and their families.

  • How about this one?

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
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 …] …]


modeling online parsing garden paths
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
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
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
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
garden path models ii

(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.



best intransitive:


transitive valence: p=0.08

garden path models ii 2
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
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
notes on the probabilistic model 2

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
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
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?
  • Concept from probability theory: marginalization
  • Complete Jurafsky 1996: modeling online data
  • Begin competition models
general idea
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
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
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
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
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
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