Productivity, Reuse, and Competition between...
Transcript of Productivity, Reuse, and Competition between...
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Productivity, Reuse, and Competition between
Generalizations
Timothy J. O’DonnellMIT
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Two Problems
1. Problem of Competition
2. Problem of Productivity
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The Problem of Competition
When multiple ways of expressing a meaning exist, how do we decide
between them?
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Competition (e.g., Aronoff, 1976; Plag, 2003; Rainer, 1988; van Marle, 1986)
• Examples
• Computed v. Stored
• goed v. went
• Computed v. Computed
• splinged v. splang (Albright & Hayes, 2003)
• Multi-way competition
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Multi-way Competition
• Hierarchical and recursive structures often give rise to multi-way competition between different combinations of stored and computed subexpression.
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Multi-way Competition (Aronoff, 1976)
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Competition Resolution• Competition is resolved in general following the
elsewhere condition (subset principle, Pāṇini’s principle, blocking, pre-emption, etc.)
• “More specific” way of expressing meaning is preferred to “more general” way.
• Variability in strength of preferences
• goed v. went
• curiosity v. curiousness, depulsiveness v. depulsivity (Aronoff & Schvaneveldt, 1978)
• tolerance v. toleration (i.e., doublets, e.g., Kiparsky, 1982a)
• More frequent items are more strongly preferred (e.g., Marcus et al. 1992)
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The Problem of Productivity
Why can some potential generalizations actually generalize productively, while others remain “inert” in existing expressions?
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Suffix
Productive (with Adjectives) -ness
Context-Dependent -ity
Unproductive -th
Productivity
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Suffix
Productive (with Adjectives) -ness
Semi-productive -ity
Unproductive -th
Productivity
circuitousness, grandness, orderliness, pretentiousness, cheapness, ...Existing:
pine-scentednessNovel: pine-scented
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Suffix
Productive (with Adjectives) -ness
Semi-productive -ity
Unproductive -th
Productivity
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Suffix
Productive (with Adjectives) -ness
Context-Dependent -ity
Unproductive -thverticality,tractability,severity, seniority, inanity, electricity, ...
Existing:
*pine-scentedityNovel:
Productivity
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Suffix
Productive (with Adjectives) -ness
Context-Dependent -ity
Unproductive -th-ile, -al, -able, -ic, -(i)an
subsequentiabilitysubsequentiable
Productivity
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Suffix
Productive (with Adjectives) -ness
Context-Dependent -ity
Unproductive -th
Productivity
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Suffix
Productive (with Adjectives) -ness
Context-Dependent -ity
Unproductive -th
warmth, width, truth, depth, ...Existing:*coolthNovel:
Productivity
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Suffix
Productive (with Adjectives) -ness
Context-Dependent -ity
Unproductive -th
Productivity
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Suffix
Most Productive -ness
Less Productive -ity
Least Productive -th
1. How can differences in productivity be represented?
2. How can differences be learned?
Productivity and Reuse
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Unifying the Problems
• Fundamental problem: How to produce/comprehend linguistic expressions under uncertainty about how meaning is conventionally encoded by combinations of stored items and composed structures.
• Productivity and competition are often just special cases of this general problem.
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Approach
• Build a model of computation and storage under uncertainty based on an inference which optimizes a tradeoff between productivity (computation) and reuse (storage).
• This implicitly explains many specific cases of productivity and competition.
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Case Studies
1. What distributional factors signal productivity?
• Explaining Baayen’s hapax-based measures.
2. How is competition resolved?
• Derives elsewhere condition.
3. Multi-way competition.
• Explains productivity and ordering generalization.
• Handles exceptional cases of paradoxical suffix combinations.
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Talk Outline
1. Introduction to productivity and reuse with Fragment Grammars (with Noah Goodman).
2. Case Studies on Productivity and Competition.
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Talk Outline
1. Introduction to productivity and reuse with Fragment Grammars (with Noah Goodman).
2. Case Studies on Productivity and Competition.
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The Framework: Three Ideas
1. Model how expressions are built by composing stored pieces.
2. Treat productivity (computation) and reuse (storage) as properties which must be determined on a case-by-case basis.
3. Infer correct patterns of storage and computation by balancing ability to predict input data against simplicity biases.
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A Simple Formal Model: Fragment Grammars
1. Formalization of the hypothesis space.
• Arbitrary contiguous (sub)trees.
2. Formalization of the inference problem.
• Probabilistic conditioning to find good balance between computation and storage.
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A Simple Formal Model: Fragment Grammars
1. Formalization of the hypothesis space.
• Arbitrary contiguous (sub)trees.
2. Formalization of the inference problem.
• Probabilistic conditioning to find good balance between computation and storage.
![Page 26: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/26.jpg)
Underlying Computational System
N
Adj
V
agree
-able
-ity
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Underlying Computational System
N
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agree
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Underlying Computational System
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Adj
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agree
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Underlying Computational System
N
Adj
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agree
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Hypothesis Space
Any contiguous subtree can be stored in memory and reused as if it were a single rule from the starting grammar.
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Hypothesis SpaceN
Adj
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agree
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Hypothesis SpaceN
Adj
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agree
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Hypothesis SpaceN
Adj
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agree
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Computation with Stored items
N
Adj
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agree
-able
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N
Adj
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Computation with Stored items
N
Adj
V
agree
-able
-ity
N
Adj
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agree
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Computation with Stored items
N
Adj
V
agree
-able
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N
Adj
V
agree
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A Simple Formal Model: Fragment Grammars
1. Formalization of the hypothesis space.
• Arbitrary contiguous (sub)trees.
2. Formalization of the inference problem.
• Probabilistic conditioning to find good balance between computation and storage.
![Page 38: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/38.jpg)
Inference Problem
Find and store the subcomputations which best predict the distribution of forms in the linguistic input taking into account prior expectations for simplicity.
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Prior Expectations
Two Opposing Simplicity Biases
1. Fewer, more reusable stored items.- Chinese Restaurant process prior on lexica.
2. Small amounts of computation.- Geometric decrease in probability in number of
random choices.
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Example Input
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Storage of Minimal, General Structures
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Computation per Expression
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Computation per Expression
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P( )
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Computation per Expression
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P( ) ×
P( )
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Computation per Expression
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Adj
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agree
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P( ) ×
P( )
P( )
×
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Sharing Across Expressions
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Adj
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agree
-able
-ness
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count
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Sharing Across Expressions
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Adj
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agree
-able
-ness
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Adj
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count
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Storage of Maximal, Specific Structures
N
Adj
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agree
-able
-ness
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Adj
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count
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Computation per Expression
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Adj
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agree
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Computation per Expression
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P( )
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Sharing Across Expressions
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-able
-ness
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Adj
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count
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Sharing Across Expressions
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agree
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-ness
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count
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Storage of Intermediate Structures
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Adj
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agree
-able
-ness
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count
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Computation per Expression
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Computation per Expression
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P( )
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Computation per Expression
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Computation per Expression
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Adj
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agree
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-ity
Thursday, February 2, 2012
P( ) ×
P( )
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Sharing Across Expressions
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
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Thursday, February 2, 2012
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Sharing Across Expressions
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
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agree
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Thursday, February 2, 2012
![Page 59: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/59.jpg)
Remarks on Inference Tradeoff
• Nothing fancy here.
• The two simplicity biases are just Bayesian prior and likelihood applied to computation and storage problem.
• Lexicon code length and data code length given lexicon in (two part) MDL.
• Can be connected with many other frameworks.
![Page 60: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/60.jpg)
Inference as Conditioning
60
• Inference Process: Probabilistic Conditioning.
• Define joint model.
P(Data, Fragments) =
P(Data | Fragments) * P(Fragments)
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Inference as Conditioning
61
• Inference Process: Probabilistic Conditioning.
• Define joint model.
P(Data, Fragments) =
P(Data | Fragments) * P(Fragments)
Likelihood(derivation probabilities)
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Inference as Conditioning
62
• Inference Process: Probabilistic Conditioning.
• Define joint model.
P(Data, Fragments) =
P(Data | Fragments) * P(Fragments)
Prior(lexicon probabilities)
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Inference as Conditioning
63
• Inference Process: Probabilistic Conditioning.
• Condition on particular dataset.
P(Fragments | Data) ∝
P(Data | Fragments) * P(Fragments)
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Probabilistic Conditioning
64
• Intuition: two-step algorithm.
1. Throw away lexicons not consistent with the data.
2. Renormalize remaining lexicons so that they sum to one.
• Maximally conservative: Relative beliefs are always conserved.
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The Mathematical Model: Fragment Grammars
• Generalization of Adaptor Grammars (Johnson et al., 2007).
• Allows storing of partial trees.
• Framework first proposed in MDL setting by De Marcken, 1996.
• Related to work on probabilistic tree-substitution grammars (e.g., Bod, 2003; Cohn, 2010; Goodman, 2003; Zuidema, 2007; Post, 2013).
![Page 66: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/66.jpg)
Talk Outline
1. Introduction to productivity and reuse with Fragment Grammars (with Noah Goodman).
2. Case Studies on Productivity and Competition.
![Page 67: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/67.jpg)
Case Studies
• Other approaches to productivity and reuse.
1. What distributions signal productivity?
2. How is competition resolved?
3. Multi-way competition.
![Page 68: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/68.jpg)
Case Studies
• Other approaches to productivity and reuse.
1. What distributions signal productivity?
2. How is competition resolved?
3. Multi-way competition.
![Page 69: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/69.jpg)
Four Strategies for Productivity and Reuse
Thursday, February 2, 2012
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Four Strategies for Productivity and Reuse
• 5 Formal Models
Thursday, February 2, 2012
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Four Strategies for Productivity and Reuse
• 5 Formal Models
• Capture historical proposals from the literature.
Thursday, February 2, 2012
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Four Strategies for Productivity and Reuse
• 5 Formal Models
• Capture historical proposals from the literature.
• Minimally different.
Thursday, February 2, 2012
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Four Strategies for Productivity and Reuse
• 5 Formal Models
• Capture historical proposals from the literature.
• Minimally different.
• Same inputs, same underlying space of representations.
Thursday, February 2, 2012
![Page 74: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/74.jpg)
Four Strategies for Productivity and Reuse
• 5 Formal Models
• Capture historical proposals from the literature.
• Minimally different.
• Same inputs, same underlying space of representations.
• State-of-the-art probabilistic models.
Thursday, February 2, 2012
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Full-Parsing (MAP Multinomial-Dirichlet Context-
Free Grammars)
- All generalizations are productive.
- Minimal abstract units.
- Johnson, et al. 2007a
- Estimated on token frequency.
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
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N
Adj
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agree
-able
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N
Adj
V
agree
-able
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Full-Parsing (FP)
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Full-Listing (MAP All-Adapted Adaptor
Grammars)- Store whole form after first use
(recursively).
- Maximally specific units.
- Johnson, et al. 2007
- Base system estimated on type frequencies.
- Formalization of classical lexical redundancy rules.
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ity
Full-Parsing (FP)
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ity
Full-Listing (FL)
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Exemplar-Based (Data-Oriented Parsing)
- Store all generalizations consistent with input.
- Two Formalization: Data-Oriented Parsing 1 (DOP1; Bod, 1998), Data-Oriented Parsing: Equal-Node Estimator (ENDOP; Goodman, 2003).
- Argued to be exemplar model of syntax.
Full-Parsing (FP)
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ity
Full-Listing (FL)
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ity
Exemplar-Based(EB)
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Inference-Based (Fragment Grammars)
- Store set of subcomputations which best explains the data.
- Formalization: Fragment Grammars (O’Donnell, et al. 2009)
- Inference depends on distribution of tokens over types.
- Only model which infers variables.
Full-Parsing (FP)
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ity
Full-Listing (FL)
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ity
Exemplar-Based(EB)
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ness
N
Adj
V
count
-able
-ity
N
Adj
V
agree
-able
-ity
N
Adj
V
agree
-able
-ity
Inference-Based(IB)
![Page 79: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/79.jpg)
Empirical Domains
Past Tense(Inflectional)
DerivationalMorphology
Productive +ed (walked) +ness (goodness)
Context-Dependent I →æ (sang) +ity (ability)
Unproductive suppletion (go/went)
+th (width)
![Page 80: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/80.jpg)
Case Studies
• Other approaches to productivity and reuse.
1. What distributions signal productivity?
2. How is competition resolved?
3. Multi-way competition.
![Page 81: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/81.jpg)
Empirical Evaluations
Past Tense DerivationalMorphology
Productive +ed (walked) +ness (goodness)
Context-Dependent I →æ (sang) +ity (ability)
Unproductive suppletion (go/went)
+th (width)
![Page 82: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/82.jpg)
What (Distributional) Cues Signal Productivity?
• Many proposals in the literature:
• Type frequency.
• Token frequency (combined with something else, e.g., entropy).
• Heterogeneity of context (generalized type frequency).
![Page 83: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/83.jpg)
Full-Listing (MAG)Full-Parsing (MDPCFG)
Inference-Based (FG)
Exemplar (ENDOP)Exemplar (DOP1)
Top 5 Most Productive Suffixes
![Page 84: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/84.jpg)
Top 5 Most Productive Suffixes
Full-Listing (MAG)Full-Parsing (MDPCFG)
Inference-Based (FG)
Exemplar (ENDOP)Exemplar (DOP1)
![Page 85: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/85.jpg)
Full-Listing (MAG)Full-Parsing (MDPCFG)
Inference-Based (FG)
Exemplar (GDMN)Exemplar (DOP1)
Top 5 Most Productive Suffixes
![Page 86: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/86.jpg)
What Evidences Productivity?
• Crucial evidence of productivity: Use of a lexical item (morpheme, rule, etc.) to generate new forms.
• Distributional consequence: Large proportion of low frequency forms.
![Page 87: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/87.jpg)
What Predicts Productivity?
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Top 5 Most Productive Suffixes
Full-Listing (MAG)Full-Parsing (MDPCFG)
Inference-Based (FG)
Exemplar (GDMN)Exemplar (DOP1)
High Proportion of Low Frequency Types
![Page 89: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/89.jpg)
Full-Listing (MAG)Full-Parsing (MDPCFG)
Inference-Based (FG)
Exemplar (GDMN)Exemplar (DOP1)
Top 5 Most Productive Suffixes
High Token Frequency
High Type Frequency
High Token Frequency
High Token Frequency
![Page 90: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/90.jpg)
• Baayen’s / (e.g., Baayen, 1992)
• Estimators of productivity based on the proportion of frequency-1 words in an input corpus.
• Various derivations.
• Rate of vocabulary change in urn model.
• Good-Turing estimation.
• Fundamentally, a rule-of-thumb.
• Only defined for single affix estimation.
Baayen’s Hapax-Based Measures
P P⇤
![Page 91: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/91.jpg)
Productivity Correlations ( values from Hay & Baayen, 2002)P/P⇤
MDPCFG(Full-parsing)
MAG(Full-listing)
DOP1(Exemplar-based)
ENDOP(Exemplar-based)
FG(Inference)
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Fragment Grammars and Hapaxes
• For the case of single affixes, Fragments Grammars behave approximately as if they were using hapaxes.
• Not an explicit assumption of the model
• Model is about how words are built. Given the fact that some new words are built, behavior arises automatically.
• Generalizes to multi-way competition.
![Page 93: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/93.jpg)
Case Studies
• Other approaches to productivity and reuse.
1. What distributions signal productivity?
2. How is competition resolved?
3. Multi-way competition.
![Page 94: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/94.jpg)
Empirical Domains
Past Tense DerivationalMorphology
Productive +ed (walked) +ness (goodness)
Context-Dependent I →æ (sang) +ity (ability)
Unproductive suppletion (go/went)
+th (width)
![Page 95: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/95.jpg)
Crucial Facts
• Defaultness: Regular rule applies when all else fails.
• Blocking: Existence of irregular blocks regular rule.
• In this domain preferences are sharp.
![Page 96: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/96.jpg)
How can Correct Inflection be Represented?
Irregulars Regulars
Thursday, February 2, 2012
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How can Correct Inflection be Represented?
Irregulars Regulars
Thursday, February 2, 2012
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−4−2
02
46
8
Correct Inflection
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
98
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
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−4−2
02
46
8
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
Preference for
Correct Past Form
99
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
Correct Inflection
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−4−2
02
46
8
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
Preference for
Incorrect Past Form 100
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
Correct Inflection
![Page 101: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/101.jpg)
−4−2
02
46
8
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
Irregulars in Training
101
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
Correct Inflection
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−4−2
02
46
8
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
Regulars in Training102
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
Correct Inflection
![Page 103: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/103.jpg)
−4−2
02
46
8
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
Regulars and Irregulars not in Training
103
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
Correct Inflection
![Page 104: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/104.jpg)
−4−2
02
46
8
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
104
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
Correct Inflection
![Page 105: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/105.jpg)
−4−2
02
46
8
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
Exemplar (Data-Oriented Parsing 1)
105
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
Correct Inflection
![Page 106: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/106.jpg)
−4−2
02
46
8
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
Full-Listing (Adaptor Grammars)
106
Correct Inflection
![Page 107: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/107.jpg)
−4−2
02
46
8
Log
Odd
s C
orre
ctIrregular ( Regular ( Unattested (
FP FPFPFL FL FLE1E1 E1E2 E2 E2IB IBIB
Inference-Based (Fragment Grammars)
107
FP Full-Parsing(Multinomial-Dirichlet CFG)
FL Full-Listing(Adaptor Grammars)
E1 Exemplar (Data-Oriented Parsing 1)
E2 Exemplar (DOP: ENDOP)
IB Inference-Based(Fragment Grammars)
Correct Inflection
![Page 108: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/108.jpg)
Why Does Blocking Occur?
• Consequence of two principles.
• Law of Conservation of Belief: Hypotheses that predict a greater variety of observed datasets place less probability on each.
• Conservativity of Conditioning: Posterior distributions have same relative probability as prior distributions.
108
![Page 109: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/109.jpg)
Law of Conservation of Belief
109
![Page 110: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/110.jpg)
Law of Conservation of Belief
110
![Page 111: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/111.jpg)
Law of Conservation of Belief
111
![Page 112: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/112.jpg)
Observation
112
x
![Page 113: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/113.jpg)
Conservativity
113
∝P(H1|D)P(H1)
∝P(H2|D)P(H2)
x
![Page 114: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/114.jpg)
Past Tense
114
![Page 115: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/115.jpg)
Elsewhere(Kiparsky, 1973; Anderson, 1969; Kiparsky, 1982a; Andrews, 1982)
• Don’t need elsewhere condition as independent stipulation (cf. subset principle, premption, etc.).
• When a choice must be made between two analyses/derivations, prefer the one with highest P(form | meaning) more “tightly.”
• More general than original statement.
• Any factor influencing P(form | meaning)
• input conditions on rules, frequency, etc.
• Stored-stored, stored-computed, computed-computed, etc.
![Page 116: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/116.jpg)
Case Studies
• Other approaches to productivity and reuse.
1. What distributions signal productivity?
2. How is competition resolved?
3. Multi-way competition.
![Page 117: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/117.jpg)
Empirical Domains
Past Tense DerivationalMorphology
Productive +ed (walked) +ness (goodness)
Context-Dependent I →æ (sang) +ity (ability)
Unproductive suppletion (go/went)
+th (width)
![Page 118: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/118.jpg)
Hierarchical Structure
• Derivational morphology hierarchical and recursive.
• Multiple suffixes can appear in a word.
![Page 119: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/119.jpg)
Many HypothesesN
Adj
V
agree
-able
-ity
![Page 120: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/120.jpg)
Many HypothesesN
Adj
V
agree
-able
-ity
![Page 121: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/121.jpg)
Many HypothesesN
Adj
V
agree
-able
-ity
![Page 122: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/122.jpg)
Empirical Problem: Suffix Ordering
• Many combinations of suffixes do not appear in words.
• Fabb (1988).
- 43 suffixes.
- 663 possible pairs (taking into account selectional restrictions)
- Only 50 exist.
![Page 123: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/123.jpg)
Empirical Problem: Suffix Ordering
• Many theories
• Level-ordering (e.g., Siegel, 1974)
• Selectional-restriction based (e.g., Plag, 2003)
• Complexity-based ordering (Hay, 2004)
• Focus on two phenomena
• Productivity and ordering generalization
• Paradoxical suffix combinations
![Page 124: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/124.jpg)
Productivity and Ordering Generalization
(Hay, 2004)
On average, more productive suffixes appear after less productive suffixes (Hay, 2002; Hay and Plag, 2004; Plag et al, 2009).
![Page 125: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/125.jpg)
Productivity and Ordering Generalization
(Hay, 2004)
• Implicit in many earlier theories (e.g., Level-Ordering Generalization of Siegel 1974).
• Hay’s argues for processing-based view (Complexity-Based Ordering)
• But: Follows as a logically necessary consequence of pattern of storage and computation.
![Page 126: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/126.jpg)
Productivity and Ordering Generalization
• Intuition:
• Less productive suffixes stored as part of words.
• More productive suffixes can attach to anything, including morphologically-complex stored forms.
![Page 127: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/127.jpg)
But: Paradoxical Suffix Combinations
• Combinations of suffixes which violate the Productivity and Ordering Generalization (as well as predictions of other earlier theories).
• -ability, -ation, -istic, -mental
![Page 128: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/128.jpg)
Multi-way Competition: -ity v. -ness
• In general, -ness more productive than -ity.
• -ity more productive after:
-ile, -able, -(i)an, -ic. (Anshen & Aronoff, 1981; Aronoff & Schvaneveldt, 1978; Cutler, 1980)
![Page 129: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/129.jpg)
Two Frequent Combinations: -ivity v. -bility
• -ive + -ity: -ivity (e.g., selectivity).
• Speaker prefer to use -ness with novel words (Aronoff & Schvaneveldt, 1978).
• depulsiveness > depulsivity.
• -ble + -ity: -bility (e.g., sensibility).
• Speakers prefer to use -ity with novel words (Anshen & Aronoff, 1981).
• remortibility > remortibleness.
![Page 130: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/130.jpg)
-ivity v. -bility
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble Full-Parsing
(MDPCFG)Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Predicted
![Page 131: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/131.jpg)
-ivity v. -bility
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble Full-Parsing
(MDPCFG)Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Predicted
Preference for -ness
![Page 132: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/132.jpg)
Full-Parsing(MDPCFG)
Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Predicted
-ivity v. -bility
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble Full-Parsing
(MDPCFG)Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Preference for -ity
![Page 133: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/133.jpg)
Full-Parsing(MDPCFG)
Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Predicted
-ivity v. -bility
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble Full-Parsing
(MDPCFG)Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Preceding suffix -ive
![Page 134: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/134.jpg)
Full-Parsing(MDPCFG)
Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Predicted
-ivity v. -bility
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble Full-Parsing
(MDPCFG)Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Preceding suffix -ble
![Page 135: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/135.jpg)
Full-Parsing(MDPCFG)
Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Predicted
Full-Parsing (Multinomial-Dirichlet Context-Free Grammar)
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble Full-Listing
(Adaptor Grammars)Exemplar
(DOP1)Exemplar
(GDMN)Inference
(FrMAGment Grammars)
![Page 136: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/136.jpg)
Full-Parsing(MDPCFG)
Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Predicted
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble Exemplar
(DOP1)Exemplar
(GDMN)Inference
(FrMAGment Grammars)
Full-Listing (Adaptor Grammars)
![Page 137: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/137.jpg)
Full-Parsing(MDPCFG)
Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Predicted Exemplar(GDMN)
Inference(FrMAGment Grammars)
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble
Exemplar-Based (Data-Oriented Parsing 1)
![Page 138: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/138.jpg)
Full-Parsing(MDPCFG)
Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(FrMAGment Grammars)
Predicted
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble
Exemplar-Based (Data-Oriented Parsing: Goodman Estimator)
![Page 139: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/139.jpg)
−50
5{{
-ness
-ity
ive ive ive ive ive iveble ble ble ble ble ble
-ive-ble Full-Parsing
(MDPCFG)Full-Listing(Adaptor Grammars)
Exemplar(DOP1)
Exemplar(GDMN)
Inference(Fragment Grammars)
Predicted
Inference-Based (Fragment Grammars)
![Page 140: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/140.jpg)
Multi-way Competition
• Explains productivity and ordering generalization.
• Explains difficult cases of competition involving paradoxical suffix combinations.
![Page 141: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/141.jpg)
Global Summary
• Inference based on distribution of tokens over types.
• Derives Baayen’s hapax-based theory.
• View the choice of whether to retrieve or compute as an inference.
• Derives elsewhere condition.
• Storage of arbitrary structures explains ordering generalizations.
• Explains Productivity and Ordering Generalization.
• Also accounts for paradoxical suffix combinations such as -ability
![Page 142: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/142.jpg)
Conclusion
• Model the problem of deriving word forms using a mixture of computation and storage as a tradeoff using standard inferential tools.
• Automatically solves many problems of productivity and competition resolution.
![Page 143: Productivity, Reuse, and Competition between Generalizationsidiom.ucsd.edu/~ebakovic/competition/slides/O...Competition Resolution • Competition is resolved in general following](https://reader033.fdocuments.in/reader033/viewer/2022060601/60550cf47336e20565351866/html5/thumbnails/143.jpg)
Thanks!