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Bayesian Network Classifiers
Class Latent Test 1 Test 2 Test 3 Test 4
On Robust Trimming of Bayesian Network Classifiers YooJung Choi and - - PowerPoint PPT Presentation
On Robust Trimming of Bayesian Network Classifiers YooJung Choi and - - PowerPoint PPT Presentation
On Robust Trimming of Bayesian Network Classifiers YooJung Choi and Guy Van den Broeck UCLA Bayesian Network Classifiers Class Latent Test 1 Test 2 Test 3 Test 4 Features Bayesian Network Classifiers Class Latent Test 1 Test 2 Test
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Bayesian Network Classifiers
Class Latent Test 1 Test 2 Test 3 Test 4
Features
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Bayesian Network Classifiers
Class Latent Test 1 Test 2 Test 3 Test 4
Features
Can we make the same classifications with fewer features?
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Why Classification Similarity?
To preserve classification behavior on individual examples
- Fairness
- Deployed classifiers
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How to measure Similarity?
What is the expected probability that a classifier α will agree with its trimming β?
“Expected Classification Agreement”
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Robust Trimming
Trimmed classifier Original classifier
Similarity
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Trimming Algorithm
“Maximum Achievable Agreement” Feature subset selection Search Objective function
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- Branch-and-Bound search
Trimming Algorithm
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- Branch-and-Bound search
- Need a bound for MAA
to prune subtrees
Trimming Algorithm
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Upper-bound for MAA
“Maximum Potential Agreement”
Maximum agreement between α and a hypothetical function that maps f’ to c
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Maximum Potential Agreement
- 1. Upper-bounds the MAA
- 2. Monotonically increasing
Great for pruning!
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Maximum Potential Agreement
- 1. Upper-bounds the MAA
- 2. Monotonically increasing
- 3. Generally easier to compute than MAA
- 4. Equal to MAA given some independence
condition (e.g. Naïve Bayes)
Great for pruning!
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𝐸 Pr 𝑆1 = + 𝐸) + 0.7 − 0.2
Computing the MPA and MAA
D
R1 R2 AC 𝑄
1 ⟺ ¬𝐸⋀¬𝑆1
𝑄2 ⟺ ¬𝐸⋀¬𝑆1 𝑄3 ⟺ ¬𝐸⋀¬𝑆1 𝑄
4 ⟺ ¬𝐸⋀¬𝑆1
𝑥 𝑄
1 = 0.7
𝑥(𝑄2) = 0.3 𝑥 𝑄3 = 0.2 𝑥(𝑄
4) = 0.8
𝑥 𝑚 = 1.0 for all other literal 𝑚
Pr(𝐸 = +) 0.2
∙∙∙ Prior works based on knowledge compilation
[Oztok,Choi,Darwiche 2016; C,Darwiche,VdB 2017]
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Evaluation
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Evaluation
Branch-and-bound improves efficiency (even with extra upper-bound computations)
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Evaluation
High information gain does not lead to high classification agreement Information-theoretic measures unaware of changes in classification threshold
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