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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

Markov Logic and Deep Networks

Pedro Domingos

Dept. of Computer Science & Eng.

University of Washington

markov logic networks

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
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
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
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
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