Structure Refinement in First Order Conditional Influence Language

Sriraam Natarajan, Weng-Keen Wong, Prasad TadepalliSchool of EECS, Oregon State University

Weighted Mean{Weighted Mean{If {task(t), doc(d), role(d,r,t)} then If {task(t), doc(d), role(d,r,t)} then t.id, r.id Qinf (Mean) d.foldert.id, r.id Qinf (Mean) d.folderIf {doc(s), doc(d), source(s,d) } then If {doc(s), doc(d), source(s,d) } then s.folder Qinf (Mean) d.folders.folder Qinf (Mean) d.folder}}

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W1 W2

“Unrolled” Network for Folder Prediction

First-order Conditional Influence Language (FOCIL)

t1.id

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s2.fr1.id r2.id t2.cd s1.ft1.cd t2.la s1.la s2.la

d.f d.f

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Prior Network

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s2.fr1.id t2.id r2.id s1.ft1.id

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Learned Network

Prior Program

Learned Program

•Conditional BIC score = -2 *CLL + dConditional BIC score = -2 *CLL + dmmlogNlogN

• Different instantiations of the same rule share parametersDifferent instantiations of the same rule share parameters

• Conditional Likelihood: EM – Maximize the joint likelihoodConditional Likelihood: EM – Maximize the joint likelihood

• CBIC score with penalty scaled downCBIC score with penalty scaled down

•Greedy Search with random restartsGreedy Search with random restarts

Scoring metric

Folder Prediction

Rank Exhaustive -R HC+RR - R Exhaustive - I HC+RR - I

1 349 354 312 311

2 107 98 128 130

3 22 26 26 26

4 15 12 20 23

5 6 4 3 4

6 0 0 1 1

7 1 4 2 0

8 0 2 1 2

9 0 0 0 0

10 0 0 0 0

11 0 0 2 3

Score 0.8299 0.8325 .7926 0.7841

Synthetic Data Set

Irrelevant attributesRelevant attributes

• Data is expensive – Exploit prior knowledge in Data is expensive – Exploit prior knowledge in structure searchstructure search

• Derived the CBIC score for our settingDerived the CBIC score for our setting

• Learned the “true” network in the synthetic Learned the “true” network in the synthetic dataset dataset

• Folder dataset: Learned the best network with Folder dataset: Learned the best network with only relevant attributesonly relevant attributes

• Folder dataset with irrelevant attributes:Folder dataset with irrelevant attributes:

Conclusions

CB I Clear ned < CB I Cbest

• Different scoring metricsDifferent scoring metrics

• BDeuBDeu• Bias/VarianceBias/Variance

• Choose the best combining rule that fits the Choose the best combining rule that fits the datadata

• Structure refinement in large real-world Structure refinement in large real-world domainsdomains

Future work

• What is the correct complexity penalty in the presence of What is the correct complexity penalty in the presence of multi-valued variables?multi-valued variables?

• Counting the # of parameters may not be the right Counting the # of parameters may not be the right solutionsolution

• What is the right scoring metric in relational setting for What is the right scoring metric in relational setting for classification?classification?

• Can the search space be intelligently pruned?Can the search space be intelligently pruned?

Issues

i X iNlmd )1(

NNXXYPCBICScorei Xd

rkm i

rlog...|(log2 ,

11,1

Weighted Mean{Weighted Mean{If {task(t), doc(d), role(d,r,t)} then If {task(t), doc(d), role(d,r,t)} then t.id, r.id Qinf (Mean) d.foldert.id, r.id Qinf (Mean) d.folderIf {doc(s), doc(d), source(s,d) } then If {doc(s), doc(d), source(s,d) } then s.folder Qinf (Mean) d.folders.folder Qinf (Mean) d.folder}}

Weighted Mean{Weighted Mean{If {task(t), doc(d), role(d,r,t)} then If {task(t), doc(d), role(d,r,t)} then t.id, r.id, t.creationDate, t.lastAccessed Qinf t.id, r.id, t.creationDate, t.lastAccessed Qinf

(Mean) d.folder (Mean) d.folderIf {doc(s), doc(d), source(s,d) } then If {doc(s), doc(d), source(s,d) } then s.folder, s.lastAccessed Qinf (Mean) d.folders.folder, s.lastAccessed Qinf (Mean) d.folder}}