Bayesian Deep Learning (BDL) gives access not only to aleatoric uncertainty, as standard neural networks already do, but also to epistemic uncertainty, a measure of confidence a model has in its own predictions. In this article, we show through experiments that the evolution of epistemic uncertainty metrics regarding the model size and the size of the training set, goes against theoretical expectations. More precisely, we observe that the epistemic uncertainty collapses literally in the presence of large models and sometimes also of little training data, while we expect the exact opposite behaviour. This phenomenon, which we call "epistemic uncertainty hole", is all the more problematic as it undermines the entire applicative potential of BDL, which is based precisely on the use of epistemic uncertainty. As an example, we evaluate the practical consequences of this uncertainty hole on one of the main applications of BDL, namely the detection of out-of-distribution samples
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）；Massachusetts Institute of Technology（麻省理工学院）
Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principl…
Cooperative Variance Estimation and Bayesian Neural Networks for Disentangling Aleatoric and Epistemic Uncertainties
Faculty of Mechanical Engineering, Delft University of Technology, Mekelweg 2, Delft, 2628 CD, The Netherlands（代尔夫特理工大学机械工程学院）；School of Engineering, Brown University, 184 Hope St., Providence, RI 02912, USA（布朗大学工程学院）
University of Munich (LMU)（慕尼黑大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Ghent University（根特大学）
Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely…
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；University of Bristol（布里斯托大学）
Typical Bayesian approaches to OOD detection use epistemic uncertainty. Surprisingly from the Bayesian perspective, there are a number of methods that successfully use aleatoric uncertainty to detect OOD points (e.g. Hendryks et al. 2018). In addition, it is difficult to use outlier exposure to improve a Bayesian OOD detection model, as it is not clear whether it is possible or desirable to increase posterior (epistemic) uncertainty at outlier points. We show that a generative model of data curation provides a principled account of aleatoric uncertainty for OOD detection. In particular, aleato…
University of Munich (LMU)（慕尼黑大学（LMU））；Munich Center for Machine Learning（慕尼黑机器学习中心）；Ghent University（根特大学）
It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, re…
The Delta method is a classical procedure for quantifying epistemic uncertainty in statistical models, but its direct application to deep neural networks is prevented by the large number of parameters $P$. We propose a low cost variant of the Delta method applicable to $L_2$-regularized deep neural networks based on the top $K$ eigenpairs of the Fisher information matrix. We address efficient computation of full-rank approximate eigendecompositions in terms of either the exact inverse Hessian, the inverse outer-products of gradients approximation or the so-called Sandwich estimator. Moreover, …
ETH Zurich（苏黎世联邦理工学院）；Google（谷歌公司）；Technical University Munich（慕尼黑工业大学）
The distribution of a neural network's latent representations has been successfully used to detect out-of-distribution (OOD) data. This work investigates whether this distribution moreover correlates with a model's epistemic uncertainty, thus indicates its ability to generalise to novel inputs. We first empirically verify that epistemic uncertainty can be identified with the surprise, thus the negative log-likelihood, of observing a particular latent representation. Moreover, we demonstrate that the output-conditional distribution of hidden representations also allows quantifying aleatoric unc…
HEC Lausanne（洛桑高等商学院）；Facebook AI Research（Facebook人工智能研究院）
We provide single-model estimates of aleatoric and epistemic uncertainty for deep neural networks. To estimate aleatoric uncertainty, we propose Simultaneous Quantile Regression (SQR), a loss function to learn all the conditional quantiles of a given target variable. These quantiles can be used to compute well-calibrated prediction intervals. To estimate epistemic uncertainty, we propose Orthonormal Certificates (OCs), a collection of diverse non-constant functions that map all training samples to zero. These certificates map out-of-distribution examples to non-zero values, signaling epistemic…
CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk
Department of Operations, HEC, University of Lausanne（洛桑大学运营管理系）；Department of Statistics, University of California, Berkeley（加州大学伯克利分校统计系）；Department of Electrical Engineering and Computer Science, University of California, Berkeley（加州大学伯克利分校电气工程与计算机科学系）；BegooAI
The belief function approach to uncertainty quantification as proposed in the Demspter-Shafer theory of evidence is established upon the general mathematical models for set-valued observations, called random sets. Set-valued predictions are the most natural representations of uncertainty in machine learning. In this paper, we introduce a concept called epistemic deep learning based on the random-set interpretation of belief functions to model epistemic learning in deep neural networks. We propose a novel random-set convolutional neural network for classification that produces scores for sets o…
University of Groningen（格罗宁根大学）；Pontifical Catholic University of Peru（秘鲁天主大学）
Neural networks are ubiquitous in many tasks, but trusting their predictions is an open issue. Uncertainty quantification is required for many applications, and disentangled aleatoric and epistemic uncertainties are best. In this paper, we generalize methods to produce disentangled uncertainties to work with different uncertainty quantification methods, and evaluate their capability to produce disentangled uncertainties. Our results show that: there is an interaction between learning aleatoric and epistemic uncertainty, which is unexpected and violates assumptions on aleatoric uncertainty, som…
Epistemic Uncertainty Quantification for Pre-trained VLMs via Riemannian Flow Matching
Department of Information Technology, Uppsala University, Uppsala, Sweden（瑞典乌普萨拉大学信息科技系）；Science for Life Laboratory, Uppsala University, Uppsala, Sweden（瑞典乌普萨拉大学生命科学实验室）
Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisition
Université de Lorraine, CentraleSupélec CNRS, LORIA, Metz, France（洛林大学、中央超导电子学学院 CNRS、LORIA、法国梅茨）；Université de technologie de Compiègne UMR CNRS 7253 Heudiasyc, France（图卢兹理工学院 UMR CNRS 7253 Heudiasyc、法国）；CNRS, Université de technologie de Compiègne UMR CNRS 7253 Heudiasyc, France（CNRS、图卢兹理工学院 UMR CNRS 7253 Heudiasyc、法国）；University of Ghent Ghent, Belgium（根特大学、比利时根特）
Evaluating deep learning models for fault diagnosis of a rotating machinery with epistemic and aleatoric uncertainty
Faculty of Engineering and Natural Sciences（工程与自然科学学院）；Department of Information and Communications Engineering（信息与通信工程系）；Department of Management, Economics and Industrial Engineering（管理、经济与工业工程系）
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…
Booz Allen Hamilton（博思艾伦汉密尔顿）；Jura Bio, Inc.（朱拉生物公司）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
The quantification of uncertainty is important for the adoption of machine learning, especially to reject out-of-distribution (OOD) data back to human experts for review. Yet progress has been slow, as a balance must be struck between computational efficiency and the quality of uncertainty estimates. For this reason many use deep ensembles of neural networks or Monte Carlo dropout for reasonable uncertainty estimates at relatively minimal compute and memory. Surprisingly, when we focus on the real-world applicable constraint of $\leq 1\%$ false positive rate (FPR), prior methods fail to reliab…
Massachusetts General Hospital（麻省总医院）；Massachusetts Institute of Technology（麻省理工学院）
As machine learning (ML) continue to be integrated into healthcare systems that affect clinical decision making, new strategies will need to be incorporated in order to effectively detect and evaluate subgroup disparities to ensure accountability and generalizability in clinical workflows. In this paper, we explore how epistemic uncertainty can be used to evaluate disparity in patient demographics (race) and data acquisition (scanner) subgroups for breast density assessment on a dataset of 108,190 mammograms collected from 33 clinical sites. Our results show that even if aggregate performance …
A Posterior-Predictive Variance Decomposition for Epistemic and Aleatoric Uncertainty in Wind Power Forecasting
School of Engineering, Deakin University（德肯大学工程学院）；ARC Training Centre in Energy Technologies for Future Grids, School of Engineering, University of Wollongong（未来电网能源技术培训中心，沃林戈大学工程学院）
A calibration test for evaluating set-based epistemic uncertainty representations
Department of Data Analysis and Mathematical Modeling（数据分析与数学建模系）；Ghent University（根特大学）；Department of Environment（环境系）；Department of Informatics（信息系）；Munich Center for Machine Learning（慕尼黑机器学习中心）；LMU Munich（慕尼黑大学）
Isik University（伊斯克大学）；Simula Research Laboratory（西穆拉研究实验室）
Deep neural network architectures are considered to be robust to random perturbations. Nevertheless, it was shown that they could be severely vulnerable to slight but carefully crafted perturbations of the input, termed as adversarial samples. In recent years, numerous studies have been conducted in this new area called "Adversarial Machine Learning" to devise new adversarial attacks and to defend against these attacks with more robust DNN architectures. However, almost all the research work so far has been concentrated on utilising model loss function to craft adversarial examples or create r…
CUPID: A Plug-in Framework for Joint Aleatoric and Epistemic Uncertainty Estimation with a Single Model
Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore（南洋理工大学李科钦医学院，新加坡）；College of Computing and Data Science, Nanyang Technological University, Singapore（南洋理工大学计算与数据科学学院，新加坡）；Centre for Medical Technologies & Innovations, National Health Group, Singapore（国家健康集团医学技术与创新中心，新加坡）
In a standard Bayesian approach to the alpha-factor model for common-cause failure, a precise Dirichlet prior distribution models epistemic uncertainty in the alpha-factors. This Dirichlet prior is then updated with observed data to obtain a posterior distribution, which forms the basis for further inferences. In this paper, we adapt the imprecise Dirichlet model of Walley to represent epistemic uncertainty in the alpha-factors. In this approach, epistemic uncertainty is expressed more cautiously via lower and upper expectations for each alpha-factor, along with a learning parameter which dete…
Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imaging
Department of Electrical and Computer Engineering, University of Rochester（电气与计算机工程系，罗切斯特大学）；Goergen Institute for Data Science & AI, University of Rochester（数据科学与人工智能研究院，罗切斯特大学）
Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks
Graduate Group in Applied Mathematics and Computational Science（应用数学与计算科学联合研究生组）；University of Pennsylvania（宾夕法尼亚大学）；Department of Mechanical Engineering and Applied Mechanics（机械工程与应用力学系）
