A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges
Deakin University（迪肯大学）；Shenzhen University（深圳大学）；Dibrugarh University（迪布鲁格尔大学）；Swinburne University of Technology（斯威本科技大学）；University of Oulu（奥卢大学）；Google Research（谷歌研究院）；University of Waterloo（滑铁卢大学）；Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）
Moloud Abdar, Farhad Pourpanah, Sadiq Hussain, Dana Rezazadegan, Li Liu, Mohammad Ghavamzadeh, Paul Fieguth, Xiaochun Cao, Abbas Khosravi, U Rajendra Acharya, V… 展开作者
Moloud Abdar, Farhad Pourpanah, Sadiq Hussain, Dana Rezazadegan, Li Liu, Mohammad Ghavamzadeh, Paul Fieguth, Xiaochun Cao, Abbas Khosravi, U Rajendra Acharya, Vladimir Makarenkov, Saeid Nahavandi
Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian approximation and ensemble learning techniques are two most widely-used UQ methods in the literature. In this regard, researchers have proposed different UQ methods and examined their performance in a variety of applications such as computer vision (e.g., self-driving cars and object detection), image processing (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring), bioinformatics, etc. This study reviews recent advances in UQ methods used in deep learning. Moreover, we also investigate the application of these methods in reinforcement learning (RL). Then, we outline a few important applications of UQ methods. Finally, we briefly highlight the fundamental research challenges faced by UQ methods and discuss the future research directions in this field.
German Research Center for Artificial Intelligence（德国人工智能研究中心）
Uncertainty quantification in neural network promises to increase safety of AI systems, but it is not clear how performance might vary with the training set size. In this paper we evaluate seven uncertainty methods on Fashion MNIST and CIFAR10, as we sub-sample and produce varied training set sizes. We find that calibration error and out of distribution detection performance strongly depend on the training set size, with most methods being miscalibrated on the test set with small training sets. Gradient-based methods seem to poorly estimate epistemic uncertainty and are the most affected by tr…
Rule-based classification models described in the language of logic directly predict boolean values, rather than modeling a probability and translating it into a prediction as done in statistical models. The vast majority of existing uncertainty quantification approaches rely on models providing continuous output not available to rule-based models. In this work, we propose an uncertainty quantification framework in the form of a meta-model that takes any binary classifier with binary output as a black box and estimates the prediction accuracy of that base model at a given input along with a le…
Bringing deep neural networks (DNNs) into safety critical applications such as automated driving, medical imaging and finance, requires a thorough treatment of the model's uncertainties. Training deep neural networks is already resource demanding and so is also their uncertainty quantification. In this overview article, we survey methods that we developed to teach DNNs to be uncertain when they encounter new object classes. Additionally, we present training methods to learn from only a few labels with help of uncertainty quantification. Note that this is typically paid with a massive overhead …
We propose a framework for the assessment of uncertainty quantification in deep regression. The framework is based on regression problems where the regression function is a linear combination of nonlinear functions. Basically, any level of complexity can be realized through the choice of the nonlinear functions and the dimensionality of their domain. Results of an uncertainty quantification for deep regression are compared against those obtained by a statistical reference method. The reference method utilizes knowledge of the underlying nonlinear functions and is based on a Bayesian linear reg…
The main objective of this paper is to outline a theoretical framework to analyse how humans' decision-making strategies under uncertainty manage the trade-off between information gathering (exploration) and reward seeking (exploitation). A key observation, motivating this line of research, is the awareness that human learners are amazingly fast and effective at adapting to unfamiliar environments and incorporating upcoming knowledge: this is an intriguing behaviour for cognitive sciences as well as an important challenge for Machine Learning. The target problem considered is active learning i…
AWS（亚马逊云科技）；Amazon（亚马逊公司）；New York University（纽约大学）
We present Fortuna, an open-source library for uncertainty quantification in deep learning. Fortuna supports a range of calibration techniques, such as conformal prediction that can be applied to any trained neural network to generate reliable uncertainty estimates, and scalable Bayesian inference methods that can be applied to Flax-based deep neural networks trained from scratch for improved uncertainty quantification and accuracy. By providing a coherent framework for advanced uncertainty quantification methods, Fortuna simplifies the process of benchmarking and helps practitioners build rob…
Pohang University of Science and Technology (POSTECH)（浦项科技大学）
We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior distribution of the parameters in deep neural networks by performing Bayesian inference on the network parameters. The posterior distribution is efficiently sampled using HMC to quantify uncertainties in the system. Several numerical examples are shown for both forward and inverse problems in high dimension to demonstrate the effectiveness of the proposed method for un…
Uncertainty quantification by ensemble learning is explored in terms of an application from computational optical form measurements. The application requires to solve a large-scale, nonlinear inverse problem. Ensemble learning is used to extend a recently developed deep learning approach for this application in order to provide an uncertainty quantification of its predicted solution to the inverse problem. By systematically inserting out-of-distribution errors as well as noisy data the reliability of the developed uncertainty quantification is explored. Results are encouraging and the proposed…
University of Connecticut（康涅狄格大学）；Tandon School of Engineering, New York University（纽约大学坦登工程学院）
Sharing information between connected and autonomous vehicles (CAVs) fundamentally improves the performance of collaborative object detection for self-driving. However, CAVs still have uncertainties on object detection due to practical challenges, which will affect the later modules in self-driving such as planning and control. Hence, uncertainty quantification is crucial for safety-critical systems such as CAVs. Our work is the first to estimate the uncertainty of collaborative object detection. We propose a novel uncertainty quantification method, called Double-M Quantification, which tailor…
Harvard Medical School（哈佛医学院）；Google Research（谷歌研究院）；Harvard School of Public Health（哈佛公共卫生学院）
Uncertainty quantification for complex deep learning models is increasingly important as these techniques see growing use in high-stakes, real-world settings. Currently, the quality of a model's uncertainty is evaluated using point-prediction metrics such as negative log-likelihood or the Brier score on heldout data. In this study, we provide the first large scale evaluation of the empirical frequentist coverage properties of well known uncertainty quantification techniques on a suite of regression and classification tasks. We find that, in general, some methods do achieve desirable coverage p…
University of Cambridge（剑桥大学）；Cancer Research UK Cambridge Centre（英国癌症研究中心剑桥中心）；Cancer Research UK Cambridge Institute（英国癌症研究中心剑桥研究所）；Danube Private University（多瑙河私立大学）；KTH Royal Institute of Technology（KTH皇家理工学院）
Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the uncertainty of the models can play a critical role for example in active learning or machine human interaction. Uncertainty quantification is especially difficult when using deep learning-based models, which are the state-of-the-art in many imaging applications. The current uncertainty quantification approaches do not scale well in high-dimensional real-world pro…
Beyond Uncertainty Quantification: Learning Uncertainty for Trust-Informed Neural Network Decisions - A Case Study in COVID-19 Classification
Faculty of Engineering & IT, University of Technology Sydney（技术悉尼大学工程与信息学院）；University Research and Innovation Center (EKIK), Óbuda University（奥布达大学研究与创新中心）
Language Technologies Institute, Carnegie Mellon University（卡内基梅隆大学语言技术研究所）；Computer Science Department, Stanford University（斯坦福大学计算机科学系）
With increasing deployment of machine learning systems in various real-world tasks, there is a greater need for accurate quantification of predictive uncertainty. While the common goal in uncertainty quantification (UQ) in machine learning is to approximate the true distribution of the target data, many works in UQ tend to be disjoint in the evaluation metrics utilized, and disparate implementations for each metric lead to numerical results that are not directly comparable across different works. To address this, we introduce Uncertainty Toolbox, an open-source python library that helps to ass…
University of Colorado Boulder（科罗拉多大学博尔德分校）；The Charles Stark Draper Laboratory, Inc.（查尔斯·斯塔克·德雷珀实验室公司）
For safe and reliable deployment in the real world, autonomous agents must elicit appropriate levels of trust from human users. One method to build trust is to have agents assess and communicate their own competencies for performing given tasks. Competency depends on the uncertainties affecting the agent, making accurate uncertainty quantification vital for competency assessment. In this work, we show how ensembles of deep generative models can be used to quantify the agent's aleatoric and epistemic uncertainties when forecasting task outcomes as part of competency assessment.
Paderborn University（帕德博恩大学）；University of Munich (LMU)（慕尼黑大学）
The idea to distinguish and quantify two important types of uncertainty, often referred to as aleatoric and epistemic, has received increasing attention in machine learning research in the last couple of years. In this paper, we consider ensemble-based approaches to uncertainty quantification. Distinguishing between different types of uncertainty-aware learning algorithms, we specifically focus on Bayesian methods and approaches based on so-called credal sets, which naturally suggest themselves from an ensemble learning point of view. For both approaches, we address the question of how to quan…
Aalborg University（奥尔堡大学）；University of Electronic Science and Technology of China（电子科技大学）；Southern University of Science and Technology（南方科技大学）
Uncertainty is an essential consideration for time series forecasting tasks. In this work, we specifically focus on quantifying the uncertainty of traffic forecasting. To achieve this, we develop Deep Spatio-Temporal Uncertainty Quantification (DeepSTUQ), which can estimate both aleatoric and epistemic uncertainty. We first leverage a spatio-temporal model to model the complex spatio-temporal correlations of traffic data. Subsequently, two independent sub-neural networks maximizing the heterogeneous log-likelihood are developed to estimate aleatoric uncertainty. For estimating epistemic uncert…
Harvard Data Science Initiative（哈佛数据科学倡议）；Harvard University（哈佛大学）
Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying uncertainty, called predictive-matching Generative Parameter Sampler (GPS). This procedure considers an Uncertainty Quantification (UQ) distribution on the targeted parameter, which matches the corresponding predictive distribution to the observed data. This framework adopts a hierarchical modeling perspective such that each observation is modeled by an individual para…
We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder-decoder network in a similar fashion to approaches considered in deep learning for image-to-image regression tasks. Since normal neural networks are data intensive and cannot provide predictive uncertainty, we propose a Bayesian approach to convolutional neural nets. A recently introduced variational gradient descent algorithm based on Stein's method is scaled to deep convolutional networks to perform approximate Baye…
Uncertainty and confidence have been shown to be useful metrics in a wide variety of techniques proposed for deep learning testing, including test data selection and system supervision.We present uncertainty-wizard, a tool that allows to quantify such uncertainty and confidence in artificial neural networks. It is built on top of the industry-leading tf.keras deep learning API and it provides a near-transparent and easy to understand interface. At the same time, it includes major performance optimizations that we benchmarked on two different machines and different configurations.
University of Oxford（牛津大学）；Microsoft Research Cambridge（微软研究院剑桥分院）
While causal models are becoming one of the mainstays of machine learning, the problem of uncertainty quantification in causal inference remains challenging. In this paper, we study the causal data fusion problem, where datasets pertaining to multiple causal graphs are combined to estimate the average treatment effect of a target variable. As data arises from multiple sources and can vary in quality and quantity, principled uncertainty quantification becomes essential. To that end, we introduce Bayesian Interventional Mean Processes, a framework which combines ideas from probabilistic integrat…
Robust data association is critical for analysis of long-term motion trajectories in complex scenes. In its absence, trajectory precision suffers due to periods of kinematic ambiguity degrading the quality of follow-on analysis. Common optimization-based approaches often neglect uncertainty quantification arising from these events. Consequently, we propose the Joint Posterior Tracker (JPT), a Bayesian multi-object tracking algorithm that robustly reasons over the posterior of associations and trajectories. Novel, permutation-based proposals are crafted for exploration of posterior modes that c…
An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression
LMU Munich（慕尼黑莱布尼茨大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；DLR-German Aerospace Center University of Tromsø（德国航空航天中心图勒大学）；German Research Center for Artificial Intelligence (DFKI, DSA)（德国人工智能研究中心）
German Research Center for Artificial Intelligence（德国人工智能研究中心）
Uncertainty in machine learning is not generally taught as general knowledge in Machine Learning course curricula. In this paper we propose a short curriculum for a course about uncertainty in machine learning, and complement the course with a selection of use cases, aimed to trigger discussion and let students play with the concepts of uncertainty in a programming setting. Our use cases cover the concept of output uncertainty, Bayesian neural networks and weight distributions, sources of uncertainty, and out of distribution detection. We expect that this curriculum and set of use cases motiva…
Seismic imaging is an ill-posed inverse problem that is challenged by noisy data and modeling inaccuracies -- due to errors in the background squared-slowness model. Uncertainty quantification is essential for determining how variability in the background models affects seismic imaging. Due to the costs associated with the forward Born modeling operator as well as the high dimensionality of seismic images, quantification of uncertainty is computationally expensive. As such, the main contribution of this work is a survey-specific Fourier neural operator surrogate to velocity continuation that m…
