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### Markov Logic and Deep Networks

Pedro Domingos

Dept. of Computer Science & Eng.

University of Washington

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

- 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.

alchemy.cs.washington.edu

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

- 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

- 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

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