A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges (original) (raw)

A Survey on Uncertainty Estimation in Deep Learning Classification Systems from a Bayesian Perspective

ACM Computing Surveys, 2022

Decision-making based on machine learning systems, especially when this decision-making can affect human lives, is a subject of maximum interest in the Machine Learning community. It is, therefore, necessary to equip these systems with a means of estimating uncertainty in the predictions they emit in order to help practitioners make more informed decisions. In the present work, we introduce the topic of uncertainty estimation, and we analyze the peculiarities of such estimation when applied to classification systems. We analyze different methods that have been designed to provide classification systems based on deep learning with mechanisms for measuring the uncertainty of their predictions. We will take a look at how this uncertainty can be modeled and measured using different approaches, as well as practical considerations of different applications of uncertainty. Moreover, we review some of the properties that should be borne in mind when developing such metrics. All in all, the ...

Evaluation of Uncertainty Quantification in Deep Learning

Information Processing and Management of Uncertainty in Knowledge-Based Systems

Artificial intelligence (AI) is nowadays included into an increasing number of critical systems. Inclusion of AI in such systems may, however, pose a risk, since it is, still, infeasible to build AI systems that know how to function well in situations that differ greatly from what the AI has seen before. Therefore, it is crucial that future AI systems have the ability to not only function well in known domains, but also understand and show when they are uncertain when facing something unknown. In this paper, we evaluate four different methods that have been proposed to correctly quantifying uncertainty when the AI model is faced with new samples. We investigate the behaviour of these models when they are applied to samples far from what these models have seen before, and if they correctly attribute those samples with high uncertainty. We also examine if incorrectly classified samples are attributed with an higher uncertainty than correctly classified samples. The major finding from this simple experiment is, surprisingly, that the evaluated methods capture the uncertainty differently and the correlation between the quantified uncertainty of the models is low. This inconsistency is something that needs to be further understood and solved before AI can be used in critical applications in a trustworthy and safe manner.

Credal Deep Ensembles for Uncertainty Quantification

2024 Conference on Neural Information Processing Systems (NeurIPS 2024), 2024

This paper introduces an innovative approach to classification called Credal Deep Ensembles (CreDEs), namely, ensembles of novel Credal-Set Neural Networks (CreNets). CreNets are trained to predict a lower and an upper probability bound for each class, which, in turn, determine a convex set of probabilities (credal set) on the class set. The training employs a loss inspired by distributionally robust optimization which simulates the potential divergence of the test distribution from the training distribution, in such a way that the width of the predicted probability interval reflects the 'epistemic' uncertainty about the future data distribution. Ensembles can be constructed by training multiple CreNets, each associated with a different random seed, and averaging the outputted intervals. Extensive experiments are conducted on various out-of-distributions (OOD) detection benchmarks (CIFAR10/100 vs SVHN/Tiny-ImageNet, CIFAR10 vs CIFAR10-C, ImageNet vs ImageNet-O) and using different network architectures (ResNet50, VGG16, and ViT Base). Compared to Deep Ensemble baselines, CreDEs demonstrate higher test accuracy, lower expected calibration error, and significantly improved epistemic uncertainty estimation.

Encoding the Latent Posterior of Bayesian Neural Networks for Uncertainty Quantification

IEEE Transactions on Pattern Analysis and Machine Intelligence

Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior distribution of the network parameters, most BNN approaches are either limited to small networks or rely on constraining assumptions such as parameter independence. These drawbacks have enabled prominence of simple, but computationally heavy approaches such as Deep Ensembles, whose training and testing costs increase linearly with the number of networks. In this work we aim for efficient deep BNNs amenable to complex computer vision architectures, e.g. ResNet50 DeepLabV3+, and tasks, e.g. semantic segmentation, with fewer assumptions on the parameters. We achieve this by leveraging variational autoencoders (VAEs) to learn the interaction and the latent distribution of the parameters at each network layer. Our approach, Latent-Posterior BNN (LP-BNN), is compatible with the recent BatchEnsemble method, leading to highly efficient (in terms of computation and memory during both training and testing) ensembles. LP-BNNs attain competitive results across multiple metrics in several challenging benchmarks for image classification, semantic segmentation and out-of-distribution detection.

Estimating uncertainty in deep learning for reporting confidence to clinicians in medical image segmentation and diseases detection

Computational Intelligence, 2020

Deep learning (DL), which involves powerful black box predictors, has achieved a remarkable performance in medical image analysis, such as segmentation and classification for diagnosis. However, in spite of these successes, these methods focus exclusively on improving the accuracy of point predictions without assessing the quality of their outputs. Knowing how much confidence there is in a prediction is essential for gaining clinicians' trust in the technology. In this article, we propose an uncertainty estimation framework, called MC‐DropWeights, to approximate Bayesian inference in DL by imposing a Bernoulli distribution on the incoming or outgoing weights of the model, including neurones. We demonstrate that by decomposing predictive probabilities into two main types of uncertainty, aleatoric and epistemic, using the Bayesian Residual U‐Net (BRUNet) in image segmentation. Approximation methods in Bayesian DL suffer from the “mode collapse” phenomenon in variational inference....

Correlated Parameters to Accurately Measure Uncertainty in Deep Neural Networks

IEEE Transactions on Neural Networks and Learning Systems

In this article, a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and, additionally, is robust to overfitting. These are commonly the two main problems classical, i.e., non-Bayesian architectures have to struggle with. The proposed approach applies variational inference in order to approximate the intractable posterior distribution. In particular, the variational distribution is defined as the product of multiple multivariate normal distributions with tridiagonal covariance matrices. Every single normal distribution belongs either to the weights or to the biases corresponding to one network layer. The layerwise a posteriori variances are defined based on the corresponding expectation values, and furthermore, the correlations are assumed to be identical. Therefore, only a few additional parameters need to be optimized compared with non-Bayesian settings. The performance of the new approach is evaluated and compared with other recently developed Bayesian methods. Basis of the performance evaluations are the popular benchmark data sets MNIST and CIFAR-10. Among the considered approaches, the proposed one shows the best predictive accuracy. Moreover, extensive evaluations of the provided prediction uncertainty information indicate that the new approach often yields more useful uncertainty estimates than the comparison methods.

Misclassification Risk and Uncertainty Quantification in Deep Classifiers

2021 IEEE Winter Conference on Applications of Computer Vision (WACV)

In this paper, we propose risk-calibrated evidential deep classifiers to reduce the costs associated with classification errors. We use two main approaches. The first is to develop methods to quantify the uncertainty of a classifier's predictions and reduce the likelihood of acting on erroneous predictions. The second is a novel way to train the classifier such that erroneous classifications are biased towards less risky categories. We combine these two approaches in a principled way. While doing this, we extend evidential deep learning with pignistic probabilities, which are used to quantify uncertainty of classification predictions and model rational decision making under uncertainty. We evaluate the performance of our approach on several image classification tasks. We demonstrate that our approach allows to (i) incorporate misclassification cost while training deep classifiers, (ii) accurately quantify the uncertainty of classification predictions, and (iii) simultaneously learn how to make classification decisions to minimize expected cost of classification errors.

Interval Deep Learning for Uncertainty Quantification in Safety Applications

Cornell University - arXiv, 2021

Deep neural networks (DNNs) are becoming more prevalent in important safetycritical applications, where reliability in the prediction is paramount. Despite their exceptional prediction capabilities, current DNNs do not have an implicit mechanism to quantify and propagate significant input data uncertainty-which is common in safety-critical applications. In many cases, this uncertainty is epistemic and can arise from multiple sources, such as lack of knowledge about the data generating process, imprecision, ignorance, and poor understanding of physics phenomena. Recent approaches have focused on quantifying parameter uncertainty, but approaches to end-to-end training of DNNs with epistemic input data uncertainty are more limited and largely problem-specific. In this work, we present a DNN optimized with gradient-based methods capable to quantify input and parameter uncertainty by means of interval analysis, which we call Deep Interval Neural Network (DINN). We perform experiments on an air pollution dataset with sensor uncertainty, and show that the DINN can produce accurate bounded estimates from uncertain input data.

Estimating Risk and Uncertainty in Deep Reinforcement Learning

ArXiv, 2019

We propose a method for disentangling epistemic and aleatoric uncertainties in deep reinforcement learning. Aleatoric uncertainty, or risk, which arises from inherently stochastic environments or agents, must be accounted for in the design of risk-sensitive algorithms. Epistemic uncertainty, which stems from limited data, is important both for risk-sensitivity and for efficient exploration. Our method combines elements from distributional reinforcement learning and approximate Bayesian inference techniques with neural networks, allowing us to disentangle both types of uncertainty on the expected return of a policy. Specifically, the learned return distribution provides the aleatoric uncertainty, and the Bayesian posterior yields the epistemic uncertainty. Although our approach in principle requires a large number of samples from the Bayesian posterior to estimate the epistemic uncertainty, we show that two networks already yield a useful approximation. We perform experiments that il...

PremiUm-CNN: Propagating Uncertainty Towards Robust Convolutional Neural Networks

IEEE Transactions on Signal Processing, 2021

Deep neural networks (DNNs) have surpassed human-level accuracy in various learning tasks. However, unlike humans who have a natural cognitive intuition for probabilities, DNNs cannot express their uncertainty in the output decisions. This limits the deployment of DNNs in mission-critical domains, such as warfighter decision-making or medical diagnosis. Bayesian inference provides a principled approach to reason about model's uncertainty by estimating the posterior distribution of the unknown parameters. The challenge in DNNs remains the multi-layer stages of non-linearities, which make the propagation of high-dimensional distributions mathematically intractable. This paper establishes the theoretical and algorithmic foundations of uncertainty or belief propagation by developing new deep learning models named PremiUm-CNNs (Propagating Uncertainty in Convolutional Neural Networks). We introduce a tensor normal distribution as a prior over convolutional kernels and estimate the variational posterior by maximizing the evidence lower bound (ELBO). We start by deriving the first-order mean-covariance propagation framework. Later, we develop a framework based on the unscented transformation (correct at least up to the second-order) that propagates sigma points of the variational distribution through layers of a CNN. The propagated covariance of the predictive distribution captures uncertainty in the output decision. Comprehensive experiments conducted on diverse benchmark datasets demonstrate: 1) superior robustness against noise and adversarial attacks, 2) self-assessment through predictive uncertainty that increases quickly with increasing levels of noise or attacks, and 3) an ability to detect a targeted attack from ambient noise.