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Markov Logic and Deep Networks. Pedro Domingos Dept. of Computer Science & Eng. University of Washington. Weight of formula i. No. of true instances of formula i in x. Markov Logic Networks. Basic idea: Use first-order logic to compactly specify large non-i.i.d. models

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Markov logic and deep networks l.jpg

Markov Logic and Deep Networks

Pedro Domingos

Dept. of Computer Science & Eng.

University of Washington

Markov logic networks l.jpg

Weight of formula i

No. of true instances of formula i in x

Markov Logic Networks

  • Basic idea: Use first-order logic tocompactly specify large non-i.i.d. models

  • MLN = Set of formulas with weights

  • Formula = Feature template (Vars→Objects)

  • E.g., HMM:

State(+s,t) ^ State(+s',t+1)

Obs(+o,t) ^ State(+s,t)

State of the art in mlns l.jpg
State of the Art in MLNs

  • Many algorithms for learning and inference

    • Inference: Millions of variables, billions of features

    • Learning: Generative, discriminative, max-margin, etc.

  • Best-performing solutions in many application areas

    • Natural language, robot mapping, social networks,computational biology, activity recognition, etc.

  • Open-source software/Web site: Alchemy

  • Book: Domingos & Lowd, Markov Logic,Morgan & Claypool, 2009.

Deep uses of mlns l.jpg
Deep Uses of MLNs

  • Very large scale inference

  • Defining architecture of deep networks

  • Adding knowledge to deep networks

  • Transition to natural language input

  • Learning with many levels of hidden variables

Mlns for deep learning l.jpg
MLNs for Deep Learning

  • Basic idea: Use small amounts of knowledgeand large amounts of joint inferenceto make up for lack of supervision

  • Relational clustering:

    • Cluster objects with similar relations to similar objects

    • Cluster relations that hold between similar sets of objects

  • Coreference resolution: Outperforms supervised approaches on MUC and ACE benchmarks

  • Semantic network extraction: Learns thousands of concepts and relations from millions of Web triples

Example unsupervised semantic parsing l.jpg
Example:Unsupervised Semantic Parsing

  • Goal: Read text and answer questions

  • No supervision or annotation

  • Input: Dependency parses of sentences(Nodes→Unary predicates / Edges→Binary preds.)

  • Outputs: Semantic parser and knowledge base

  • Basic idea: Cluster expressions with similar subexpressions

  • Maps syntactic variants to common meaning

  • Discovers its own meaning representation

  • “Part of” lattice of clusters

  • Applied to corpus of biomedical abstracts

  • Three times more correct answers than next best