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## Robust Textual Inference via Graph Matching

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**Robust Textual Inference viaGraph Matching**Aria Haghighi Andrew Ng Christopher Manning**Textual Entailment Examples**• TEXT (T): A Filipino hostage in Iraq was released. • HYPOTHESIS (H): A Filipino hostage was freed in Iraq. • Entailed • Only Need Lexical Similarity Matching**Another Example**• T: The Psychobiology Institute of Israel was established in 1979. • H: Israel was established in 1979. • Not Entailed • Must go beyond matching only words**The Need For Relations**• H: Israel was founded in 1971. • T: The Psychobiolgy Institute of Israel was founded in 1971. • No match for important relation in H! • Must match words and relations between them**Our Approach**• Dependency Graph • Represent words / phrases as vertices and edges as syntactic / semantic relations • Graph Matching • Approximate notion of Isomorphism • H is entailed from T if the cost of matching H to T low.**Phrase Structure Parse**S NP VP PP John’s mother walked to the store. Representation Pipeline Raw Text John’s mother walked to the store. • Modified parser of [Klein and Manning ‘03] • Handle collocations: John rang_up Mary**walked**(VBD) to subj mother (NN) store (NN) poss John (NNP) Representation Pipeline Phrase Structure Parse Dependency Tree S NP VP PP John’s mother walked to the store. • Modified Collins’ Head Rules • Typed relations via tgrep expressions**Representation Pipeline**• Local dependencies not enough • Additional Analysis • Semantic Role Labeling [Toutanova et al ‘05] • Named Entity Recognition: Collapse named entities into single vertex [Finkel et al ‘04] • Coreference Resolution: • T: Since its formation in 1948, Israel … • H: Israel was established in 1948.**Matching Example**Hypothesis Text**Cost Model**• Matching: Amapping from vertices of Hto those of T (and NULL vertex) • Cost of matching H to T determined by lowest cost matching**Vertex Cost Model**• Penalize for each vertex substitution**Vertex Substitution**• VertexSub(v,M(v)) • Exact Match • Synonym Match • Hypernym Match: v is a “kind of” M(v) • WordNet Similarity (Resnik Measure) • Distributional Similarity • Part-Of-Speech Match**Vertex Weight**• Weights for Vertex Importance • Part-Of-Speech • Named Entity Type • TF-IDF**Relation Matching**• Partial Match (and Stem Match) • T: The Japanese invasion of Manchuria. • H: Japan invaded Manchuria. • Ancestor Match • T: John is studying French farming practices. • H: John is studying French farming.**Relation Cost**• For each edge e in H,is the image under M, a path in T • Weigh each edge according to “importance” of typed relation**Cost Model**• PathSub(v v’, M(v) M(v’)) • Exact Match: Matching preserves edge and edge label • Partial Match: Match preserves edge but not label • Ancestor Match: M(v) is an ancestor of M(v’) • Kinked Match: M(v) and M(v’) share a common ancestor • Costs Scale with Length of Path**Final Cost Model**• Combine VertexCost and RelationCost**Matching Example**Hypothesis Text**Finding Minimal Matching**• With VertexCost only, minimal matching found with Bipartite Graph Matching • NP-Hard: RelationCost(M) = 0 if and only if H isomorphic to sub-graph of T • Approximate Search • Initialize M to best matching using only VertexCost(M) [Bipartite Graph Matching] • Do Greedy Hill-climbing with full cost model • Seems to do well in practice**Learning Weights**• Parameterize Substitution Costs • Problem: We don’t know matchings in training data. If we did, training would be easy. • Solution: Alternate between finding matchings and re-estimating parameters**Experiments**• Data: Recognizing Textual Entailment ‘05 [Dagan et al, ‘05] • 567 Development Pairs • 800 Test Pairs • CWS = Confidence Weighted Score**Problem Cases**• Monotonicity Assumptions • Superlatives • T: Osaka is the tallest tower in western Japan. • H: Osaka is the tallest tower in Japan. • Non-Factive Verbs • T: It is rumored that John is dating Sally. • H: John is dating Sally.**Conclusions**• What’s been done • Learned Graph Matching framework • New edge and vertex features • Fast effective search procedure • What’s Needed? More Resources! • Lexical Resources: Problems with Recall • Better Dependency Parsing • Measures of Phrasal Similarity**Thanks!**Aria Haghighi Andrew Ng Christopher Manning**Examples**• T: C and D Technologies announced that it has closed the acquisition of Datel Inc. • H: Datel Acquired C and D technologies. • Not Entailed • Recognize switch in argument structure. • Note nominilization**Textual Entailment**• Problem Definition • Given text and hypothesis (T,H) • Determine if H ‘follows’ from T ? • Not strict logical entailment • Applications • Information Extraction • Question Answering