I. Motivation & Basics

Why consider uncertainty?

• Reliability and dependability requirements in industrial systems
• Low acceptable range for wrong predictions or decisions
• This differs from "Web-ML" applications where wrong predictions are often acceptable/accepted
• Most state-of-the-art "Web-ML" approaches ignore uncertainty

Example "Web-ML" VS "Industry-ML"

• Web-ML: Wrong classification of a male website visitor as female $\rightarrow$ display of "wrong category" advertisement
• Industry-ML: Wrong classification of a medical lesion image $\rightarrow$ malignant cancer stays undetected

Current Situation

Standard Deep Learning (DL) methods do not provide information about the uncertainty of their predictions

• Reason: The neural networks (NN) produce point estimates
• Implicit assumption: The point estimate is representative
  (This could be wrong, e.g. bc of multimodality, more later)

Basics

Basic Premise: Models are used to perform statistical inference
Problem: Predictions are prone to noise, wrong model inference & inductive assumptions

• Learning Phase: Optimization & Prediction
• Approaches: (Approximate) Bayesian & Ensemble Learning
• Application Fields: Computer Vision, Image Processing, Medical Image Analysis, Natural Language Processing, Reinforcement Learning (e.g. Robotics), Active Learning

Multimodality toy example:

• Sinus $\rightarrow$ unimodal
• Inverse Sinus $\rightarrow$ multimodal
• Classic NN (using MSE as loss) fails
• Common solution approach: Mixture Density Networks (MDNs)

II. Uncertainty Modelling Techniques

Dropout

• Dropout was initially introduced to combat overfitting in DNNs $^{[1]}$
• Idea: During Training, randomly drop (i.e. apply an independent random Bernoulli mask to the) activations of the NN (except output layer)
• Has become one of the most popular modern approaches to regularization in deep learning

VI using different divergences

• Possible solution to Problem 2: Use alpha-divergences as alternative to VI's KL objective

• This avoids VI's uncertainty underestimation

• Hernandez-Lobato: Black-box alpha divergence $^{[2]}$

• Yingzhen and Gal: Dropout inference in Bayesian neural networks with alpha-divergences $^{[3]}$

Alternative approaches

• Bayes by Backprop: Blundell, Charles, et al. "Weight Uncertainty in Neural Network." International Conference on Machine Learning. 2015.
• An alternative approach to VI was recently presented that tries to efficiently compute the Bayesian posterior:
  • Dusenberry, Michael W., et al. "Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors." arXiv preprint arXiv:2005.07186 (2020).

Ensemble Techniques

Simple and scalable predictive uncertainty estimation using deep ensembles
- Lakshminarayanan, Pritzel, Blundell (2017) $^{[1]}$

One of the first works to apply ensemble ideas to deep NNs in order to investigate predictive uncertainty performance:

• proposes an alternative to Bayesian NNs
• simple to implement
• readily parallelizable
• requires very little hyperparameter tuning
• yields high quality predictive uncertainty estimates

Details

• For regression tasks, use a network that outputs $\mu(x)$ and $\sigma(x)$
• Treat the observed values as samples from a (heteroscedastic) Gaussian
• Train by minimizing the negative log-likelihood:

• Coding detail: Enforce positivity of the $\sigma(x)$ output neuron! $^{[1]}$
• To get the final prediction, the ensemble is treated as a uniformly-weighted mixture model (i.e. predictions/predicted class probabilities are averaged)

What are scoring rules?

• Scoring rules measure the quality of predictive uncertainty
• They assigns a numerical score to a predictive distribution $p(y|x)$, with better calibrated predictions receiving higher scores

Proper scoring rules:

• minimizing NLL (Negative log likelihood, note: equal to softmax cross entropy loss)
• Brier score (equivalent to the MSE between predicted probabilities and one-hot labels)

Generalization:

• We also want generalization of the predictive uncertainty to domain shift (aka out-of-distribution (OOD) data)
• $\rightarrow$ measure if the network knows what it knows

Results in Lakshminarayanan et al.: $^{[1]}$

Out-of-distribution (OOD) results on ImageNet

• ImageNet trained only on dogs
• Tested on non-dogs
• Ensemble performs as expected:
  • Predictive entropy is a lot higher for the unknown classes (non-dogs), i.e. the model is uncertain
  • while max. predicted probability is lower

OOD on MNIST:

• Trained on MNIST, tested on combined MNIST (known) and NotMNIST (unknown) data
• Deep ensembles perform robust
• MC Dropout produces overconfident wrong predictions
• (This matches previous observation that VI can underestimate uncertainty)

Bootstrap Ensemble

• Bootstrapped DQN (Deep Q-Network) proposed as efficient ensemble architecture $^{[1]}$
• Single NN $\rightarrow$ ensemble members share most weights
• Output-Layer is split into so-called "heads", representing the individual ensemble outputs
• Bootstrap training procedure implemented by using boolean mask $\rightarrow$ training data set of each member differs slightly

III. Applications & Evaluations

The power of ensembles for active learning in image classification

CVPR 2018 (Authors from Bosch Center for Artificial Intelligence)

• Compare ensemble-based architectures against Monte-Carlo Dropout

Results:

• Ensemble-based uncertainties outperform other methods of uncertainty estimation (in particular MC Dropout)

"We find that the difference in active learning performance can be explained by a combination of decreased model capacity and lower diversity of MC Dropout ensembles"

Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision

CVPR 2020 (ETH Zürich & Uppsala University)

• Confirm that ensembling consistently outperforms MC Dropout and provides more reliable and practical uncertainty estimates
• Depth Completion & Semantic Segmentation tasks
• Attribute the success of ensembling to its ability to capture multi-modality present in the posterior distribution

Other fields of application

RL

• Kahn: "Uncertainty-aware reinforcement learning for collision avoidance" (Bootstrapping & Dropout)
• Osband: "Deep exploration via bootstrapped DQN" as well as follow-up work
• Sedlmeier: "Uncertainty-based Out-of-Distribution Classification in Deep Reinforcement Learning"

Medical

• Leveraging uncertainty information from deep neural networks for disease detection https://www.nature.com/articles/s41598-017-17876-z

Thank you! Questions?