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Learning Logistic Circuits

Learning Logistic Circuits. Yitao Liang, Guy Van den Broeck. January 31, 2019. Which model to choose. Neural Networks:. Classical AI Methods:. Hungry?. $25?. Sleep?. Restaurant?. …. “Black Box” Good performance on Image Classification. Clear Modeling Assumption. 1. SPN.

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Learning Logistic Circuits

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  1. Learning Logistic Circuits Yitao Liang, Guy Van den Broeck January 31, 2019

  2. Which model to choose Neural Networks: Classical AI Methods: Hungry? $25? Sleep? Restaurant? • … • “Black Box” • Good performance on Image Classification • Clear Modeling Assumption 1

  3. SPN Starting Point: Probabilistic Circuits A promising synthesis of the two State-of-the-art on Density Estimation 2

  4. What if we only want to learn a classifier 3

  5. Logical Circuits 1 1 0 Input: 1 1 0 1 0 1 0 0 = 1 AND 0 1 0 1 1 0 0 1 0 Bottom-up Evaluation 0 1 1 0 0 1 4

  6. Logical -> Probabilistic Circuits Red Parameters: Conditional Probabilities 5

  7. Logical -> Probabilistic Circuits Input: 0 0.096 1 0 0.096 0.194 0.24= 0.8*0.3 0.01 0.24 0.00 0.1= 0.1*1 + 0.9*0 0.0 0.3 0.1 0.8 Multiply the parameters bottom-up 0 1 0 1 1 0 0 0 1 0 6

  8. Evaluate Logistic Circuits Input: 0 1 Multiply the parameters bottom-up Logistic function on final output 0 1 1 0 0 1 7

  9. Are logistic circuits amenable to tractable learning 8

  10. Special Case: Logistic Regression Logistic Regression What about other logistic circuits in more general forms? 9

  11. Parameter Learning “Hot” wires are active features 10

  12. Parameter Learning Due to decomposability and determinism, reduce to logistic regression Features associated with each wire “Global Circuit Flow” Convex Parameter learning 11

  13. Structure Learning Similar to LearnPsdd Split nodes to reduce variance of gradients 12

  14. Comparable Accuracy with Neural Nets 13

  15. Significantly Smaller in Size 14

  16. Better Data Efficiency 15

  17. Probabilistic -> Logistic Circuits Probabilities become log-odds Discriminative Counterparts 16

  18. What do Features Mean This is the feature that contributes the most to this image’s classification probability feature value : 0.925 feature weight : 3.489 feature interpretation: curvy lines and hallow center 17

  19. Conclusion Logistic circuits: • Synthesis of symbolic AI and statistical learning • Discriminative counterparts of probabilistic circuits • Convex parameter learning • Simple heuristic for structure learning • Good performance • Easy to interpret 18

  20. Thanks https://github.com/UCLA-StarAI/LogisticCircuit

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