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A Confidence Model for Syntactically-Motivated Entailment Proofs

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### A Confidence Model for Syntactically-Motivated Entailment Proofs

### Thank you

Asher Stern & Ido Dagan

ISCOL

June 2011, Israel

Recognizing Textual Entailment (RTE)

- Given a text, T, and a hypothesis, H
- Does T entail H

Example

- T: An explosion caused by gas took place at a Taba hotel
- H: A blast occurred at a hotel in Taba.

Proof Over Parse Trees

T = T0→ T1→ T2→ ... →Tn = H

Bar Ilan Proof System

H: A blast occurred at a hotel in Taba.

An explosion caused by gas took place at a Taba hotel

A blast caused by gas took place at a Taba hotel

A blast took place at a Taba hotel

A blast occurred at a Taba hotel

A blast occurred at a hotel in Taba.

Lexical

Lexical syntactic

Syntactic

Tree-Edit-Distance

Insurgents attacked soldiers -> Soldiers were attacked by insurgents

Proof over parse trees

Which steps?

How to classify?

Decide “yes” if and only if a proof was found

Almost always “no”

Cannot handle knowledge inaccuracies

Estimate a confidence to the proof correctness

- Tree-Edits
- Regular or custom
- Entailment Rules

Proof systems

TED based

Entailment Rules based

Linguistically motivated

Rich knowledge

No estimation of proof correctness

Incomplete proofs

Mixed system with ad-hoc approximate match criteria

- Estimate the cost of a proof
- Complete proofs
- Arbitrary operations
- Limited knowledge

Our System

- The benefits of both worlds, and more!
- Linguistically motivated complete proofs
- Confidence model

Our Method

- Complete proofs
- On the fly operations
- Cost model
- Learning model parameters

On the fly Operations

- “On the fly” operations
- Insert node on the fly
- Move node / move sub-tree on the fly
- Flip part of speech
- Etc.
- More syntactically motivated than Tree Edits
- Not justified, but:
- Their impact on the proof correctness can be estimated by the cost model.

Cost Model

- Represent a proof as F(P) = (F1, F2 … FD)
- Define weight vector w=(w1,w2,…,wD)
- Define proof cost
- Classify a proof
- b is a threshold
- Learn the parameters (w,b)

Search Algorithm

- Need to find the “best” proof
- “Best Proof” = proof with lowest cost
- Assuming a weight vector is given
- Search space is exponential
- pruning

Parameter Estimation

- Goal: find good weight vector and threshold (w,b)
- Use a standard machine learning algorithm (logistic regression or linear SVM)
- But: Training samples are not given as feature vectors
- Learning algorithm requires training samples
- Training samples construction requires weight vector
- Learning weight vector done by learning algorithm
- Iterative learning

Parameter Estimation

- Start with w0, a reasonable guess for weight vector
- i=0
- Repeat until convergence
- Find the best proofs and construct vectors, using wi
- Use a linear ML algorithm to find a new weight vector, wi+1
- i = i+1

Conclusions

- Linguistically motivated proofs
- Complete proofs
- Cost model
- Estimation of proof correctness
- Search best proof
- Learning parameters
- Results
- Reasonable behavior of learning scheme

Q & A

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