Conditional Independence in Testing Bayesian Networks Yujia Shen, - - PowerPoint PPT Presentation

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Conditional Independence in Testing Bayesian Networks Yujia Shen, - - PowerPoint PPT Presentation

Jun 20, 2023 533 likes •641 views

Computer Automated Reasoning Science Group Conditional Independence in Testing Bayesian Networks Yujia Shen, Haiying Huang, Arthur Choi, Adnan Darwiche. Computer Science Department, UCLA Computer Science Department Conditional Independence

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Computer Science Department Conditional Independence in Testing Bayesian Networks

Computer Science Department, UCLA

Yujia Shen, Haiying Huang, Arthur Choi, Adnan Darwiche.

Conditional Independence in Testing Bayesian Networks

Computer Science

Automated Reasoning Group

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Computer Science Department Conditional Independence in Testing Bayesian Networks

  • Neural networks are universal approximators.
  • They are data hungry.

DEEP LEARNING

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Fuse Knowledge with Expressiveness

Sampled functions that are represented using a simple neural network. Feature Pr (Label | Feature)

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Computer Science Department Conditional Independence in Testing Bayesian Networks

  • BNs utilize data efficiently using conditional independence assumptions.

BAYESIAN NETWORKS

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Fuse Knowledge with Expressiveness

X Y Z

λ¯

x

* λx * λ¯

y

* * λy * * θ¯

x

θx θ¯

z|¯ x

* θz|¯

x

* θ¯

z|x

* θz|x * θ¯

y|¯ x

θy|¯

x

θ¯

y|x

θy|x * * + + + + P ?(¯ z) P ?(z)

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SLIDE 4

Computer Science Department Conditional Independence in Testing Bayesian Networks

  • BNs utilize data efficiently using conditional independence assumptions.
  • Marginal queries are not universal approximators.

EXPRESSIVENESS IN BAYESIAN NETWORKS

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Fuse Knowledge with Expressiveness

Ground truth Best fit for BN

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Computer Science Department Conditional Independence in Testing Bayesian Networks

  • Testing Bayesian networks are universal approximators [Choi, Darwiche(2018)].

TESTING BAYESIAN NETWORK

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Fuse Knowledge with Expressiveness

Ground truth Best fit for BN Best fit for TBN Universal Approximator

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Computer Science Department Conditional Independence in Testing Bayesian Networks

  • TBN represents a set of distributions.
  • Different evidence selects different distribution for inference.

A SET OF DISTRIBUTIONS

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Testing Bayesian Network

X Y Z

Prx=0.2,y=0.2(z = 1 | x = 0.2, y = 0.2)

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Prx=0.6,y=0.4(z = 1 | x = 0.6, y = 0.4)

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Computer Science Department Conditional Independence in Testing Bayesian Networks June 9, 2019 7

Conditional Independence in TBN

Suppose X is d-separated from Y given Z. In classical Bayesian networks, Pr(x|yz) = Pr(x|z)

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In testing Bayesian networks,

Pryz(x|yz) =Prz(x|z)

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Pryz

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Prz

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is the joint distribution selected under evidence yz is the joint distribution selected under evidence z . .

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Computer Science Department Conditional Independence in Testing Bayesian Networks June 9, 2019 8

Fuse Knowledge with Expressiveness

Testing Bayesian Networks Model Assumptions Bayesian Networks Universal Approximators Neural Networks

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Computer Science Department Conditional Independence in Testing Bayesian Networks

Thank You Thank You Thank You

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Conditional Independence in Testing Bayesian Networks