The Most Probable Explanation for Probabilistic Logic Programs with - - PowerPoint PPT Presentation

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The Most Probable Explanation for Probabilistic Logic Programs with - - PowerPoint PPT Presentation

May 24, 2023 586 likes •988 views

The Most Probable Explanation for Probabilistic Logic Programs with Annotated Disjunctions Dimitar Shterionov , Joris Renkens, Jonas Vlasselaer, Angelika Kimmig, Wannes Meert, Gerda Janssens ILP 2014 (Nancy, France) 1 3 1 2 0.6 0.3

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The Most Probable Explanation for Probabilistic Logic Programs with Annotated Disjunctions

Dimitar Shterionov, Joris Renkens, Jonas Vlasselaer, Angelika Kimmig, Wannes Meert, Gerda Janssens

ILP 2014 (Nancy, France)

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0.6 0.3 0.1 0.5 0.1 0.4 0.2 0.5 0.3

1 2 3

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0.6 0.3 0.1 0.5 0.1 0.4 0.2 0.5 0.3 Yes/No 0.6/0.4 Yes/No 0.6/0.4 Yes/No 0.6/0.4

1 2 3

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1 2 3

0.6 0.3 0.1 0.5 0.1 0.4 0.2 0.5 0.3 Yes/No 0.6/0.4 Yes/No 0.6/0.4 Yes/No 0.6/0.4

What is most probable to happen?

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1 2 3

0.6 0.3 0.1 0.5 0.1 0.4 0.2 0.5 0.3 No 0.4

What is most probable to happen?

No 0.4 No 0.4

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What is most probable to happen knowing the player always picks? 1 2 3

0.6 0.3 0.1 0.5 0.1 0.4 0.2 0.5 0.3 Yes/No 0.6/0.4 Yes/No 0.6/0.4 Yes/No 0.6/0.4

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1 2 3

0.6 0.5 0.5 Yes 0.6

What is most probable to happen knowing the player always picks?

Yes 0.6 Yes 0.6

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The Most Probable Explanation

  • Useful for

– Medical Diagnostics – Computer Systems Diagnostics – Scheduling – etc.

  • Typical task in SRL and PGM
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Outline

  • ProbLog programs with Annotated Disjunctions
  • MPE of ProbLog programs
  • Encodings of Annotated Disjunctions
  • Evaluation
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Outline

  • ProbLog programs with Annotated Disjunctions
  • MPE of ProbLog programs
  • Encodings of Annotated Disjunctions
  • Evaluation
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ProbLog*

* http://dtai.cs.kuleuven.be/problog/

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Possible Worlds

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Probabilistic Facts

0.6 0.3 0.1 Yes/No 0.6/0.4

1

Can express Cannot express

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Probabilistic Facts

0.6 0.3 0.1 Yes/No 0.6/0.4

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Can express Cannot express but annotated disjunctions can

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Logic Programs with Annotated Disjunctions

Probability Tree

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Outline

  • ProbLog programs with Annotated Disjunctions
  • MPE of ProbLog programs
  • Encodings of Annotated Disjunctions
  • Evaluation
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ProbLog

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ProbLog

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Logic Programs with Annotated Disjunctions

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Logic Programs with Annotated Disjunctions

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Outline

  • ProbLog programs with Annotated Disjunctions
  • MPE of ProbLog programs
  • Encodings of Annotated Disjunctions
  • Evaluation
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ProbLog Encoding of ADs

  • ADs converted to Facts and Rules.
  • Negation retains the mutual exclusiveness.
  • Incorrect for MPE.
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Weighted CNF Encoding of ADs

  • Surrogate Probabilistic Facts
  • Rules
  • Constraints

(based on cProbLog implementation)

  • Retains the AD semantics regardless the task.
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Weighted CNF Encoding of ADs

...

True False

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… and Constraints in CNF (to retain the mutual exclusiveness)

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Possible Worlds of the WMC Encoding

s p f ( 1 , r , 1 ) spf(1,g,2) spf(1,b,3) spf(2,p,1) s p f ( 2 , n p , 2 )

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s p f ( 1 , r , 1 ) spf(1,g,2) spf(1,b,3) spf(2,p,1) s p f ( 2 , n p , 2 )

Possible Worlds of the WMC Encoding

1:1 correspondence

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s p f ( 1 , r , 1 ) spf(1,g,2) spf(1,b,3) spf(2,p,1) s p f ( 2 , n p , 2 )

Trust me it's correct

Possible Worlds of the WMC Encoding

1:1 correspondence

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Possible Worlds and MPE

s p f ( 1 , r , 1 ) spf(1,g,2) spf(1,b,3) spf(2,p,1) s p f ( 2 , n p , 2 )

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Outline

  • ProbLog programs with Annotated Disjunctions
  • MPE of ProbLog programs
  • Encodings of Annotated Disjunctions
  • Evaluation
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Outline

  • ProbLog programs with Annotated Disjunctions
  • MPE of ProbLog programs
  • Encodings of Annotated Disjunctions
  • Evaluation
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ProbLog vs Weighted CNF Encoding - Time

Balls

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ProbLog vs Weighted CNF Encoding - Time

Balls

Growing Negated Body Growing Heads

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ProbLog vs Weighted CNF Encoding - Size

Balls

Growing Negated Body Growing Heads

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MPE - Time

Growing Negated Body

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Outline

  • ProbLog programs with Annotated Disjunctions
  • MPE of ProbLog programs
  • Encodings of Annotated Disjunctions
  • Evaluation
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Conclusions

  • WMC encoding of Annotated Disjunctions

– Constraints – Semantically correct

  • (Efficient) MPE is possible
  • Good performance
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Thank you! Merci!