Understanding Deep Generative Bayesian Networks in Machine Learning

Exploring the differences between Neural Networks and Bayesian Neural Networks, the advantages of the latter including robustness and adaptation capabilities, the Bayesian theory behind these networks, and insights into the comparison with regular neural network theory. Dive into the complexities, uncertainties, and potential benefits of Bayesian Neural Networks for machine learning applications.

• Machine Learning
• Bayesian Networks
• Neural Networks
• Bayesian Theory
• Uncertainties

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Uploaded on Nov 26, 2024 | 0 Views

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1. Deep Generative Bayesian Network 1

2. Summary 1. Neural Networks vs Bayesian Neural Networks 2. Advantages of Bayesian Neural Networks 3. Bayesian Theory 4. Preliminary Results 2

3. 1 Neural Networks vs Bayesian Neural Networks 3

4. Regular Neural Networks Fixed weights and biases Kinda boring One set of features: one result 4

5. Bayesian Neural Network Gaussian distributions Awesome Monte Carlo sampling The weights and biases are drawn following these distributions One set of features: different results possible 5

6. 2 Advantages of Bayesian Neural Networks 6

7. Advantages vs Disadvantages Robust to small datasets (less prone to More computer demanding overfitting) Implementation more difficult Conscious of its uncertainties More complexe theory Gives a probability distribution as an output Can adapt easily to regular neural networks architectures 7

8. 3 Bayesian Theory 8

9. Comparison to Regular Neural Network Theory Minimize the loss: Regular theory Equivalent to maximizing the likelihood: Calculate the posterior distribution: Bayesian theory Baye s rules (exact inference): 9

10. Approximation Posterior distribution Parametrized distribution Kullbach-Liebler divergence: 10

11. Loss function Evidence Lower BOund (ELBO): 11

12. 4 Custom dataset 12

13. Building custom rings True ring Adding noise to the dataset The goal is to reproduce this noise Noised ring 13

14. The noise distribution Depends on the features: mean, width, position, angles Make the model fit to this distribution 14

15. Fitting the noise distribution Working first on a simpler distribution By minimizing the ELBO loss we can fit the distribution - - blue = predicted distribution orange = true distribution 15

16. Updates 16

17. No convergence - - blue = predicted distribution orange = true distribution 17

18. Partial convergence - - blue = predicted distribution orange = true distribution 18

19. Discrete probability distribution Real distribution - - blue = predicted distribution orange = true distribution 19

20. The CODE 20

21. The CODE 21

22. Image loss and KL loss - - blue = factor switch orange = kl_factor adjust 22