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Learning, Logic, and Probability: a Unified View

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- Markov logic networks (MLNs) combine first-order logic and probabilistic graphical models by assigning weights to first-order logic formulas. This allows logical knowledge bases to represent soft constraints rather than hard rules. - MLNs can be represented as templates for Markov networks, where each grounding of a first-order formula corresponds to a feature. Inference involves extracting a minimal grounded subnetwork and using MCMC methods. Learning maximizes the pseudo-likelihood of the data. - The speaker experiments with MLNs on a university database, finding they outperform hand-built knowledge bases, ILP, and other statistical relational learning systems on tasks like predicting student-advisor relationships.

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Learning, Logic, and Probability: A Unified View Pedro Domingos Dept. Computer Science & Eng. University of Washington (Joint work with Stanley Kok, Matt Richardson and Parag Singla)
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Way Things Were ,[object Object],[object Object],[object Object],[object Object]
The Way Things Are ,[object Object],[object Object],[object Object],[object Object],[object Object]
The Way Things Will Be ,[object Object],[object Object],[object Object],[object Object],[object Object]
State of the Art ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Learning + Logic + Probability ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Questions ,[object Object],[object Object],[object Object]
Markov Logic Networks ,[object Object],[object Object],[object Object],[object Object],[object Object]
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Markov Networks ,[object Object],B D C A ,[object Object]
Markov Networks ,[object Object],B D C A ,[object Object],Weight of Feature i Feature i
First-Order Logic ,[object Object],[object Object],[object Object]
Example of First-Order KB Friends either both smoke or both don’t smoke Smoking causes cancer
Example of First-Order KB
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Markov Logic Networks ,[object Object],[object Object],[object Object]
Definition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example of an MLN Cancer(A) Smokes(A) Smokes(B) Cancer(B) Suppose we have two constants: Anna (A) and Bob (B)
Example of an MLN Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Suppose we have two constants: Anna (A) and Bob (B)
Example of an MLN Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Suppose we have two constants: Anna (A) and Bob (B)
Example of an MLN Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Suppose we have two constants: Anna (A) and Bob (B)
More on MLNs ,[object Object],[object Object],[object Object],[object Object],[object Object]
MLNs Subsume FOL ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Inference ,[object Object],[object Object],[object Object],[object Object]
Grounding the Template ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
Probabilistic Inference ,[object Object],[object Object],[object Object],[object Object]
Markov Chain Monte Carlo ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Learning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Learning Weights ,[object Object],[object Object],[object Object],Feature count according to data Feature count according to model
Pseudo-Likelihood [Besag, 1975] ,[object Object],[object Object],[object Object],[object Object]
MLN Weight Learning ,[object Object],[object Object],[object Object],[object Object],where nsat i (x=v) is the number of satisfied groundings of clause i in the training data when x takes value v
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Domain ,[object Object],[object Object],[object Object],[object Object],[object Object]
Systems Compared ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Sample Clauses in KB ,[object Object],[object Object],[object Object],[object Object],[object Object]
Methodology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Results 0.04 -0.166 0.02 -0.095 BN 0.19 -0.059 0.17 -0.218 NB 0.04 -0.371 0.03 -0.255 CL 0.08 -0.067 0.16 -0.124 KB 0.03 -0.852 0.02 -0.341 MLN(CL) 0.20 -0.043 0.25 -0.047 MLN(KB) 0.25 -0.040 0.27 -0.044 MLN(KB+CL) Area CLL Area CLL Partial Info All Info System
Results: All Info
Results: Partial Info
Efficiency ,[object Object],[object Object],[object Object],[object Object],[object Object]
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Related Work ,[object Object],[object Object],[object Object],[object Object],[object Object]
Special Cases of Markov Logic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Future Work: Inference ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Future Work: Learning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Future Work: Applications ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Conclusion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Learning, Logic, and Probability: a Unified View

  • 1. Learning, Logic, and Probability: A Unified View Pedro Domingos Dept. Computer Science & Eng. University of Washington (Joint work with Stanley Kok, Matt Richardson and Parag Singla)
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  • 14. Example of First-Order KB Friends either both smoke or both don’t smoke Smoking causes cancer
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  • 19. Example of an MLN Cancer(A) Smokes(A) Smokes(B) Cancer(B) Suppose we have two constants: Anna (A) and Bob (B)
  • 20. Example of an MLN Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Suppose we have two constants: Anna (A) and Bob (B)
  • 21. Example of an MLN Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Suppose we have two constants: Anna (A) and Bob (B)
  • 22. Example of an MLN Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Suppose we have two constants: Anna (A) and Bob (B)
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  • 28. Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
  • 29. Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
  • 30. Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
  • 31. Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
  • 32. Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
  • 33. Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
  • 34. Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
  • 35. Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
  • 36. Example Grounding P( Cancer(B) | Smokes(A), Friends(A,B), Friends(B,A)) Cancer(A) Smokes(A) Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B)
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  • 49. Results 0.04 -0.166 0.02 -0.095 BN 0.19 -0.059 0.17 -0.218 NB 0.04 -0.371 0.03 -0.255 CL 0.08 -0.067 0.16 -0.124 KB 0.03 -0.852 0.02 -0.341 MLN(CL) 0.20 -0.043 0.25 -0.047 MLN(KB) 0.25 -0.040 0.27 -0.044 MLN(KB+CL) Area CLL Area CLL Partial Info All Info System
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