Semantic Role Labeling via Integer Linear Programming Inference

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Semantic Role Labeling via Integer Linear
Programming Inference

• Vasin Punyakanok, Dan Roth, Wen-tau Yih, Dav
  Zimak
• Department of Computer Science
• University of Illinois at Urbana-Champaign

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Semantic Role Labeling

• Semantic parsing is an important task toward
  natural language understanding, and has immediate
  applications in Q/A.
• For each verb in a sentence
• identify all constituents that fill a semantic
  role
• determine their roles
• Agent, Patient or Instrument,
• Their adjuncts, e.g., Locative, Temporal or
  Manner
• PropBank project Kingsbury Palmer02 provides
  a large human-annotated corpus of semantic
  verb-argument relations.
• CoNLL-2004 shared task Carreras Marquez 04
• No parsed data in the input

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Example

• A0 represents the leaver,
• A1 represents the thing left,
• A2 represents the benefactor,
• AM-LOC is an adjunct indicating the location of
  the action,
• V determines the verb.

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Special Argument Types

• C-XXX (continuity)

• R-XXX (relative pronoun)

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3-Stage Approach

• Find potential argument candidates
• Filtering most of the phrases
• Classify arguments to types
• Estimate the conditional probabilities
• Inference for Argument Structure
• Cost Function
• Constraints
• Integer linear programming (ILP)

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I. Find Potential Arguments

• An argument can be any set of consecutive words

• Restrict potential arguments
• Classify BEGIN(word)
• BEGIN(word) 1 ? word begins argument
• Classify END(word)
• END(word) 1 ? word ends argument
• Argument
• (wi,...,wj) is a potential argument iff
• BEGIN(wi) 1 and END(wj) 1

• Reduce set of potential arguments (PotArg)

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II. Arguments Type Likelihood

• Assign type-likelihood
• How likely is it that arg a is type t?
• For all a ? POTARG , t ? T
• P (argument a type t )

0.3 0.2 0.2 0.3
0.6 0.0 0.0 0.4
A0
C-A1
A1
Ø
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Details Phrase-level Classifier

• Learn a classifier (SNoW)
• ARGTYPE(arg)
• ?P(arg) ? A0,A1,...,C-A0,...,AM-LOC,...
• argmaxt?A0,A1,...,C-A0,...,LOC,... wt ?P(arg)
• Estimate Probabilities
• Softmax over SNoW activations
• P(a t) exp(wt ?P(a)) / Z

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Inference

• Maximize the expected number of correct argument
  predictions
• T argmaxT ? i P( ai ti )
• Subject to some constraints
• Structural and Linguistic (R-A1?A1)

I left my nice pearls to her
I left my nice pearls to her
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Problem Setting

• Random Variables X
• Conditional Distributions P (learned by
  classifiers)
• Constraints C any Boolean function
• defined on partial assignments (possible
  weights W on constraints)
• Goal Find the best assignment
• The assignment that achieves the highest global
  accuracy.
• This is an Integer Programming Problem

z
XargmaxX P?X subject to
constraints C
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Integer Linear Programming

• A set of binary variables, x (x1,, xd)
• A cost vector p ?Rd,
• Cost matrices C1?Rd?Rt C2?Rd?Rr,
• t, r of (inequality, equality) constraints d
  - of variables.
• The ILP solution x is the vector that maximizes
  the cost function,
• x argmax x ?0,1d p?x
• Subject to C2xgt b1 and C1x b2,
• where b1, b2?Rd and x?0,1d

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LP Formulation Linear Cost

• Cost function
• ?a ? POTARG P(at) ?a ? POTARG , t ? T P(at)
  xat
• Indicator variables
• xa1A0, xa1 A1, , xa4 AM-LOC, xP4? ?
  0,1
• Total Cost
• p(a1 A0) x(a1 A1) p(a1 ?) x(a1 ?)
  p(a4 ?) x(a4 ?)

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Linear Constraints (1/2)

• Binary values
• ? a ? POTARG , t ? T , xa t ? 0,1
• Unique labels
• ? a ? POTARG , ? t ? T xa t 1
• No overlapping or embedding
• a1 and a2 overlap ? xa1Ø xa2Ø ? 1

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Linear Constraints (2/2)

• No duplicate argument classes
• ?a ? POTARG xa A0 ? 1
• R-XXX
• ? a2 ? POTARG , ?a ? POTARG xa A0 ? xa2
  R-A0
• C-XXX
• a2 ? POTARG , ? (a ? POTARG) ? (a is before a2 )
  xa A0 ? xa2 C-A0
• Exactly one argument of type Z (e.g, verb)
• Given a verb, no argument types will not appear.
• Any Boolean Rule can be encoded as a linear
  constraint.

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Experiments (1/2)

• Without inference, the sentence level prediction
  is usually meaningless.
• The key point of the experiments is to evaluate
  the role of inference.

I. Given the boundaries of arguments
Development Set
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Experiments (2/2)
II. Effects of inference on different stages
Provides better probability estimations

• Overall F1 on Test Set 66.39
• 2nd best system in the CoNLL-2004 shared task

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Summary

• Inference Global inference helps !
• All constraints vs. only non-overlapping
  constraints
• error reduction gt 5 gt 1 absolute F1
• A lot of room for improvement (additional
  constraints)
• Easy and fast 1520 minutes
• The ILP Inference framework is also applied in
  other problems.
• Allows the use of soft constraints
• Possible to interleave learning and inference and
  deal with interacting learning problems

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Argument Types

• A0-A5 and AA have different semantics for each
  verb as specified in the PropBank Frame files.
• 13 types of adjuncts labeled as AM-XXX where XXX
  specifies the adjunct type.
• C-XXX is used to specify the continuity of the
  argument XXX.
• In some cases, the actual agent is labeled as the
  appropriate argument type, XXX, while the
  relative pronoun is instead labeled as R-XXX.