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

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 0.1 0.5 0.1 0.4 0.2 0.5 0.3 2

Yes/No Yes/No Yes/No 0.6/0.4 0.6/0.4 0.6/0.4 3 1 2 0.6 0.3 0.1 0.5 0.1 0.4 0.2 0.5 0.3 3

Yes/No Yes/No Yes/No 0.6/0.4 0.6/0.4 0.6/0.4 3 1 2 0.6 0.3 0.1 0.5 0.1 0.4 0.2 0.5 0.3 What is most probable to happen? 4

No No No 0.4 0.4 0.4 3 1 2 0.6 0.3 0.1 0.5 0.1 0.4 0.2 0.5 0.3 What is most probable to happen? 5

Yes/No Yes/No Yes/No 0.6/0.4 0.6/0.4 0.6/0.4 3 1 2 0.6 0.3 0.1 0.5 0.1 0.4 0.2 0.5 0.3 What is most probable to happen knowing the player always picks ? 6

Yes Yes Yes 0.6 0.6 0.6 3 1 2 0.6 0.5 0.5 What is most probable to happen knowing the player always picks ? 7

The Most Probable Explanation ● Useful for – Medical Diagnostics – Computer Systems Diagnostics – Scheduling – etc. ● Typical task in SRL and PGM 8

Outline ● ProbLog programs with Annotated Disjunctions ● MPE of ProbLog programs ● Encodings of Annotated Disjunctions ● Evaluation 9

ProbLog* 11 * http://dtai.cs.kuleuven.be/problog/

Possible Worlds 12

Probabilistic Facts Yes/No 0.6/0.4 Can express 1 Cannot express 0.6 0.3 0.1 13

Probabilistic Facts Yes/No 0.6/0.4 Can express 1 Cannot express but annotated disjunctions can 0.6 0.3 0.1 14

Logic Programs with Annotated Disjunctions Probability Tree 15

ProbLog 18

ProbLog 19

Logic Programs with Annotated Disjunctions 20

Logic Programs with Annotated Disjunctions 21

ProbLog Encoding of ADs ● ADs converted to Facts and Rules. ● Negation retains the mutual exclusiveness. ● Incorrect for MPE. 23

Weighted CNF Encoding of ADs ● Surrogate Probabilistic Facts ● Rules ● Constraints (based on cProbLog implementation) ● Retains the AD semantics regardless the task. 24

Weighted CNF Encoding of ADs False True ... 25

… and Constraints in CNF (to retain the mutual exclusiveness) 26

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 ) 27

1:1 correspondence 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 ) 28

1:1 correspondence 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 ) Trust me it's correct 29

s p f ( 1 Possible Worlds and MPE , r , 1 ) spf(1,g,2) spf(1,b,3) spf(2,p,1) s p f ( 2 , n p , 2 ) 30

ProbLog vs Weighted CNF Encoding - Time Balls 33

ProbLog vs Weighted CNF Encoding - Time Balls Growing Negated Body 34 Growing Heads

ProbLog vs Weighted CNF Encoding - Size Balls Growing Negated Body 35 Growing Heads

MPE - Time Growing Negated Body 36

Conclusions ● WMC encoding of Annotated Disjunctions – Constraints – Semantically correct ● (Efficient) MPE is possible ● Good performance 38

Thank you! Merci! 39

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

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