dynamic probabilistic relational models paper by: sumit sanghai, pedro domingos, daniel weld anna...
TRANSCRIPT
Dynamic Probabilistic Relational Models
Paper by: Sumit Sanghai, Pedro Domingos, Daniel Weld
Anna Yershova
Presentation slides are adapted from: Lise Getoor, Eyal Amir and Pedro Domingos slides
Limitations of the DBNs
How to represent: • Classes of objects and multiple instances of a
class • Multiple kinds of relations • Relations evolving over time
Example: Early fault detection in manufacturing Complex and diverse relations evolving over the manufacturing process.
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Fault detection in manufacturing
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BRACKETweightshapecolor
welded tobolt
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BOLTweightsizetype
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ACTION
action
Strain s1
Patient p1
Patient p2
Contactc3
Contactc2
Contactc1
Strain s2
Patient p3
Strain
Patient
Contact
DPRM with AU Semantics
)).(|.(),S,|( ,.
AxparentsAxPP Sx Ax
I
AttributesObjects
probability distribution over completions I:
2TPRM relational skeletons 12+ =
Strain
Patient
Contact
Strain s1
Patient p1
Patient p2
Contactc3
Contactc2
Contactc1
Strain s2
Patient p3
The Objective of PF
• The objective of the particle filter is to compute the conditional distribution
• To do this analytically - expensive• The particle filter gives us an approximate
computational technique.
Particle Filter Algorithm
• Create particles as samples from the initial state distribution p(A1, B1, C1).
• For i going from 1 to N– Update each particle using the state update
equation.– Compute weights for each particle using the
observation value.– (Optionally) resample particles.
Another Issue
• Rao-Blackwellising the relational attributes can vastly reduce the size of the state space.
• If the relational skeleton contains a large number of objects and relations, storing and updating all the requisite probabilities can still become quite expensive.
• Use some particular knowledge of the domain
Abstraction trees
• Replace the vector of probabilities with a tree structure
• leaves represent probabilities for entire sets of objects
• nodes represent all combinations of the propositional attributes
Part21 - pf
Uniform distr. over the rest of the objects
trueP(Part1.mate | Bolt(Part1, Part2))
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Experiments
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BOLTweightsizetype
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ACTION
action
Dom(ACTION.action) ={paint, drill, polish,Change prop. Attr.,Change rel. Attr.}
Fault Model Used
With probability 1 pf an action produces the intended effect, with probability pf one of the several faults occur:
• Painting not being completed
• Wrong color used
• Bolting the wrong object
• Welding the wrong object
Observation Model Used
With probability 1 po the truth value of the attribute is observed, with probability po an incorrect value is observed
Measure of the Accuracy
• K-L divergence between distributions
• Computing is infeasible – approximation is needed
Approximation of K-L Divergence
• We are interested only in measuring the differences in performance of different approximation methods -> first term is eliminated
• Take S samples from the true distribution (S = 10,000 in the experiments)
Experimental Results
• Abstraction trees reduced RBPF’s time and memory by a factor of 30 to 70
• On average six times longer and 11 times the memory of PF, per particle.
• However, note that we ran PF with 40 times more particles than RBPF.
• Thus, RBPF is using less time and memory than PF, and performing far better in accuracy.