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

Outline ● ProbLog programs with Annotated Disjunctions ● MPE of ProbLog programs ● Encodings of Annotated Disjunctions ● Evaluation 10

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

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Outline ● ProbLog programs with Annotated Disjunctions ● MPE of ProbLog programs ● Encodings of Annotated Disjunctions ● Evaluation 17

ProbLog 18

ProbLog 19

Logic Programs with Annotated Disjunctions 20

Logic Programs with Annotated Disjunctions 21

Outline ● ProbLog programs with Annotated Disjunctions ● MPE of ProbLog programs ● Encodings of Annotated Disjunctions ● Evaluation 22

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

Outline ● ProbLog programs with Annotated Disjunctions ● MPE of ProbLog programs ● Encodings of Annotated Disjunctions ● Evaluation 31

Outline ● ProbLog programs with Annotated Disjunctions ● MPE of ProbLog programs ● Encodings of Annotated Disjunctions ● Evaluation 32

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

Outline ● ProbLog programs with Annotated Disjunctions ● MPE of ProbLog programs ● Encodings of Annotated Disjunctions ● Evaluation 37

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

Thank you! Merci! 39