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t1.id. r1.id. t1.cd. t1.la. T2.id. r2.id. t2.la. s1.la. s1.f. t2.cd. s2.la. r1.id. t1.id. t2.id. s1.f. s2.f. s2.f. r2.id. t1.id. r1.id. t2.id. r2.id. C. W. W. B. I. C. C. B. I. C.
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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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r1.id t2.id r2.ids1.folder
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W1 W2
“Unrolled” Network for Folder Prediction
First-order Conditional Influence Language (FOCIL)
t1.id
d.f
d.f
s2.fr1.id r2.id t2.cd s1.ft1.cd t2.la s1.la s2.la
d.f d.f
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t1.la T2.id
Prior Network
d.f
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s2.fr1.id t2.id r2.id s1.ft1.id
d.f d.f
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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}}
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