Uncertainty Modeling in Deep Learning
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1. Y. Gal, Uncertainty in Deep Learning, 2016 2. P. McClure, Representing Inferential Uncertainty in Deep Neural Networks Through Sampling, 2017 3. G. Khan et al., Uncertainty-Aware Reinforcement Learning from Collision Avoidance, 2016 4. B. Lakshminarayanan et al., Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles, 2017 5. A. Kendal and Y. Gal, What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?, 2017 6. S. Choi et al., Uncertainty-Aware Learning from Demonstration Using Mixture Density Networks with Sampling-Free Variance Modeling, 2017 7. Anonymous, Bayesian Uncertainty Estimation for Batch Normalized Deep Networks, 2017
![Kendal (2017)
36
Aleatoric & epistemic uncertainties
ˆW ⇠ q(W)
x
ˆy ˆW(x) ˆ2
ˆW
(x)
[ˆy, ˆ2
] = f
ˆW
(x)
L =
1
N
NX
i=1
log N(yi; ˆy ˆW(x), ˆ2
ˆW
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![Kendal (2017)
37
Aleatoric & epistemic uncertainties
ˆW ⇠ q(W)
x
ˆy ˆW(x) ˆ2
ˆW
(x)
[ˆy, ˆ2
] = f
ˆW
(x)
Var(y) ⇡
1
T
TX
t=1
ˆy2
t
TX
t=1
ˆyt
!2
+
1
T
TX
t=1
ˆ2
t
Epistemic unct. Aleatoric unct,](https://image.slidesharecdn.com/uncertaintyindeeplearning-171216053607/85/Uncertainty-Modeling-in-Deep-Learning-37-320.jpg)
![Kendal (2017)
38
Heteroscedastic uncertainty as loss attenuation
ˆW ⇠ q(W)
x
ˆy ˆW(x) ˆ2
ˆW
(x)
[ˆy, ˆ2
] = f
ˆW
(x)](https://image.slidesharecdn.com/uncertaintyindeeplearning-171216053607/85/Uncertainty-Modeling-in-Deep-Learning-38-320.jpg)
![[PR12] You Only Look Once (YOLO): Unified Real-Time Object Detection](https://cdn.slidesharecdn.com/ss_thumbnails/yolo-170616085751-thumbnail.jpg?width=560&fit=bounds)
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Uncertainty Modeling in Deep Learning
- 1. Survey of Uncertainties in Deep Learning in a nutshell Sungjoon Choi CPSLAB, SNU
- 2. Introduction 2 The first fatality from an assisted driving system
- 3. Introduction 3 Google Photos identified two black people as 'gorillas'
- 4. Contents 4
- 5. 5 Y. Gal, Uncertainty in Deep Learning, 2016
- 6. Gal (2016) 6 Dropout as a Bayesian approximation
- 7. Gal (2016) 7 Dropout as a Bayesian approximation
- 8. Gal (2016) 8 Dropout as a Bayesian approximation
- 9. Gal (2016) 9 Bayesian Neural Network p(y⇤ |x⇤ , X, Y) = Z p(y⇤ |x⇤ , w)p(w|X, Y)dwInference p(w|X, Y)Posterior
- 10. Gal (2016) 10 Bayesian Neural Network p(y⇤ |x⇤ , X, Y) = Z p(y⇤ |x⇤ , w)p(w|X, Y)dwInference p(w|X, Y)Posterior Variational Inference KL (q✓(w)||p(w|X, Y)) = Z q✓(w) log q✓(w) p(w|X, Y) dw ELBO Z q✓(w) log p(Y|X, w)dw KL(q✓(w)||p(w)) ELBO (reparametrization) Z p(✏) log p(Y|X, w)d✏ KL(q✓(w)||p(w)) w = g(✓, ✏)
- 11. Gal (2016) 11 Bayesian Neural Network with dropout
- 12. Gal (2016) 12 Bayesian Neural Network with dropout
- 13. Gal (2016) 13 Model uncertainty 1. Given a model trained with several pictures of dog breeds, a user asks the model to decide on a dog breed using a photo of a cat.
- 14. Gal (2016) 14 Model uncertainty 2. We have three different types of images to classify, cat, dog, and cow, where only cat images are noisy.
- 15. Gal (2016) 15 Model uncertainty 3. What is the best model parameters that best explain a given dataset? what model structure should we use?
- 16. Gal (2016) 16 Model uncertainty 1. Given a model trained with several pictures of dog breeds, a user asks the model to decide on a dog breed using a photo of a cat. 2. We have three different types of images to classify, cat, dog, and cow, where only cat images are noisy. 3. What is the best model parameters that best explain a given dataset? what model structure should we use?
- 17. Gal (2016) 17 Model uncertainty 1. Given a model trained with several pictures of dog breeds, a user asks the model to decide on a dog breed using a photo of a cat. 2. We have three different types of images to classify, cat, dog, and cow, where only cat images are noisy. 3. What is the best model parameters that best explain a given dataset? what model structure should we use? Out of distribution test data Aleatoric uncertainty Epistemic uncertainty
- 18. Gal (2016) 18 Predictive mean and uncertainties
- 19. 19 P. McClure, Representing Inferential Uncertainty in Deep Neural Networks Through Sampling, 2017
- 20. McClure (2017) 20 Different variational distributions
- 21. McClure (2017) 21 Results on MNIST
- 22. 22 G. Khan et al., Uncertainty-Aware Reinforcement Learning from Collision Avoidance, 2016
- 23. Khan (2016) 23 Uncertainty-Aware Reinforcement Learning Uncertainty-aware collision prediction model
- 24. Khan (2016) 24 Uncertainty-Aware Reinforcement Learning Uncertainty is based on bootstrapped neural networks using dropout
- 25. Khan (2016) 25 Uncertainty-Aware Reinforcement Learning Uncertainty is based on bootstrapped neural networks using dropout Bootstrapping - Generate multiple datasets using sampling with replacement. - The intuition behind bootstrapping is that, by generating multiple populations and training one model per population, the models will agree in high-density areas (low uncertainty) and disagree in low-density areas (high uncertainty).
- 26. Khan (2016) 26 Uncertainty-Aware Reinforcement Learning Uncertainty is based on bootstrapped neural networks using dropout Bootstrapping - Generate multiple datasets using sampling with replacement. - The intuition behind bootstrapping is that, by generating multiple populations and training one model per population, the models will agree in high-density areas (low uncertainty) and disagree in low-density areas (high uncertainty). Dropout - Dropout can be viewed as an economical approximation of an ensemble method (such as bootstrapping) in which each sampled dropout mask corresponds to a different model.
- 27. Khan (2016) 27 Uncertainty-Aware Reinforcement Learning
- 28. 28 B. Lakshminarayanan et al., Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles, 2017
- 29. Lakshminarayanan (2017) 29 Proper scoring rule A scoring rule assigns a numerical score to a predictive distribution rewarding better calibrated predictions over worse. (…) It turns out many common neural network loss functions are proper scoring rules.
- 30. Lakshminarayanan (2017) 30 Density network x µ✓(x) ✓(x) L = 1 N NX i=1 log N(yi; µ✓(xi), 2 ✓(xi)) f✓(x)
- 31. Lakshminarayanan (2017) 31 Adversarial training with a fast gradient sign method Adversarial training can be also be interpreted as a computationally efficient solution to smooth the predictive distributions by increasing the likelihood of the target around an neighborhood of the observed training examples.
- 33. Lakshminarayanan (2017) 33 Proposed method Empirical variance (5) Density network (1) Adversarial training Deep ensemble (5)
- 34. 34 A. Kendal and Y. Gal, What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?, 2017
- 35. Kendal (2017) 35 Aleatoric & epistemic uncertainties
- 36. Kendal (2017) 36 Aleatoric & epistemic uncertainties ˆW ⇠ q(W) x ˆy ˆW(x) ˆ2 ˆW (x) [ˆy, ˆ2 ] = f ˆW (x) L = 1 N NX i=1 log N(yi; ˆy ˆW(x), ˆ2 ˆW (x))
- 37. Kendal (2017) 37 Aleatoric & epistemic uncertainties ˆW ⇠ q(W) x ˆy ˆW(x) ˆ2 ˆW (x) [ˆy, ˆ2 ] = f ˆW (x) Var(y) ⇡ 1 T TX t=1 ˆy2 t TX t=1 ˆyt !2 + 1 T TX t=1 ˆ2 t Epistemic unct. Aleatoric unct,
- 38. Kendal (2017) 38 Heteroscedastic uncertainty as loss attenuation ˆW ⇠ q(W) x ˆy ˆW(x) ˆ2 ˆW (x) [ˆy, ˆ2 ] = f ˆW (x)
- 40. 40 S. Choi et al., Uncertainty-Aware Learning from Demonstration Using Mixture Density Networks with Sampling-Free Variance Modeling, 2017
- 41. Choi (2017) 41 Mixture density networks x µ1(x) µ2(x) µ3(x)⇡1(x) ⇡2(x) ⇡3(x) 1(x) 2(x) 3(x) f ˆW(x) L = 1 N NX i=1 log KX j=1 ⇡j(xi)N(yi; µj(xi), 2 j (x))
- 42. 42 Choi (2017) Mixture density networks
- 43. 43 Choi (2017) Explained and unexplained variance We propose a sampling-free variance modeling method using a mixture density network which can be decomposed into explained variance and unexplained variance.
- 44. 44 Choi (2017) Explained and unexplained variance In particular, explained variance represents model uncertainty whereas unexplained variance indicates the uncertainty inherent in the process, e.g., measurement noise.
- 45. 45 Choi (2017) Explained and unexplained variance We present uncertainty-aware learning from demonstration by using the explained variance as a switching criterion between trained policy and rule- based safe mode. Unexplained Variance Explained Variance
- 47. 47 Anonymous, Bayesian Uncertainty Estimation for Batch Normalized Deep Networks, 2017
- 48. Anonymous (2018?) 48 Monte Carlo Batch Normalization (MCBN)
- 49. Anonymous (2018?) 49 Batch normalized deep nets as Bayesian modeling Learnable parameter Stochastic parameter
- 50. Anonymous (2018?) 50 Batch normalized deep nets as Bayesian modeling
- 51. Anonymous (2018?) 51 MCBN to Bayesian SegNet
- 52. 52 ) ( . )