Heinz Nixdorf Institute（海因茨·尼克斯多夫研究所）；Paderborn University（帕德博恩大学）；UMR CNRS 7253 Heudiasyc（法国国家科学研究中心联合研究单位7253 Heudiasyc）；Sorbonne Universités（索邦大学）；Université de Technologie de Compiègne（贡比涅技术大学）
Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for which its current prediction is maximally uncertain. The predictions as well as the measures used to quantify the degree of uncertainty, such as entropy, are almost exclusively of a probabilistic nature. In this paper, we advocate a distinction between two different types of uncertainty, referred to as epistemic and aleatoric, in the context of active learning. Roughly speaking, these notions capture the reducible and the irreducible part of the total uncertainty in a prediction, respectively. We conjecture that, in uncertainty sampling, the usefulness of an instance is better reflected by its epistemic than by its aleatoric uncertainty. This leads us to suggest the principle of "epistemic uncertainty sampling", which we instantiate by means of a concrete approach for measuring epistemic and aleatoric uncertainty. In experimental studies, epistemic uncertainty sampling does indeed show promising performance.
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…
Technical University Munich（慕尼黑工业大学）；Autonomous Intelligent Driving GmbH（自主智能驾驶有限公司）；Google（谷歌）
We present a sampling-free approach for computing the epistemic uncertainty of a neural network. Epistemic uncertainty is an important quantity for the deployment of deep neural networks in safety-critical applications, since it represents how much one can trust predictions on new data. Recently promising works were proposed using noise injection combined with Monte-Carlo sampling at inference time to estimate this quantity (e.g. Monte-Carlo dropout). Our main contribution is an approximation of the epistemic uncertainty estimated by these methods that does not require sampling, thus notably r…
Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last couple of years. In particular, the idea of distinguishing between two important types of uncertainty, often refereed to as aleatoric and epistemic, has recently been studied in the setting of supervised learning. In this paper, we propose to quantify these uncertainties with random forests. More specifically, we show how two general approaches for measurin…
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…
The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this …
Kansas State University（堪萨斯州立大学）；ETH Zurich（苏黎世联邦理工学院）
Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN stemming from modeling errors and measurement uncertainty. We consider aleatoric uncertainty in the form of probabilistic links and noise in feature vector of nodes, while epistemic uncertainty is incorporated via a probability distribution over the model parameters. We propose a unified approach to treat both sources of uncertainty in a Bayesian framework, …
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…
Epistemic Uncertainty in Conformal Scores: A Unified Approach
Department of Statistics Federal University of São Carlos（统计系巴西圣卡洛斯联邦大学）；Institute of Mathematics and Computer Science University of São Paulo（数学与计算机科学研究所圣保罗大学）
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, …
CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）；University College London（伦敦大学学院）；Inria（法国国家信息与自动化研究所）；Gatsby Computational Neuroscience Unit（盖茨计算神经科学单元）；University of Adelaide（阿德莱德大学）
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 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…
Technical University of Munich（慕尼黑工业大学）；Munich Data Science Institute（慕尼黑数据科学研究所）；Stanford University（斯坦福大学）；Stanford Intelligent Systems Laboratory（斯坦福智能系统实验室）
Characterizing aleatoric and epistemic uncertainty on the predicted rewards can help in building reliable reinforcement learning (RL) systems. Aleatoric uncertainty results from the irreducible environment stochasticity leading to inherently risky states and actions. Epistemic uncertainty results from the limited information accumulated during learning to make informed decisions. Characterizing aleatoric and epistemic uncertainty can be used to speed up learning in a training environment, improve generalization to similar testing environments, and flag unfamiliar behavior in anomalous testing …
College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机与软件工程学院）；The Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen University（深圳大学广东省智能信息处理重点实验室）；College of Mathematics and Statistics, Shenzhen University（深圳大学数学与统计学院）；Department of Mathematics, The Chinese University of Hong Kong（香港中文大学数学系）
Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more data or refining the learning models. Over the last few years, scholars have proposed many epistemic uncertainty handling techniques which can be roughly grouped into two categories, i.e., Bayesian and ensemble. This paper provides a comprehensive review of epistemic uncertainty learning techniques in supervised learning over the last five years. As such, we…
Optimal Conformal Prediction under Epistemic Uncertainty
LMU Munich（慕尼黑莱茵姆大学）；CISPA（Cybersecurity Institute for Safer Applications）；LMU Munich MCML（慕尼黑莱茵姆大学MCML）；Ghent University（根特大学）；University of Cologne（科隆大学）；DFKI（德国达姆施塔特研究所）
Curricula for goal-conditioned reinforcement learning agents typically rely on poor estimates of the agent's epistemic uncertainty or fail to consider the agents' epistemic uncertainty altogether, resulting in poor sample efficiency. We propose a novel algorithm, Query The Agent (QTA), which significantly improves sample efficiency by estimating the agent's epistemic uncertainty throughout the state space and setting goals in highly uncertain areas. Encouraging the agent to collect data in highly uncertain states allows the agent to improve its estimation of the value function rapidly. QTA uti…
Osaka university（大阪大学）；The University of Tokyo（东京大学）
Bayesian deep learning plays an important role especially for its ability evaluating epistemic uncertainty (EU). Due to computational complexity issues, approximation methods such as variational inference (VI) have been used in practice to obtain posterior distributions and their generalization abilities have been analyzed extensively, for example, by PAC-Bayesian theory; however, little analysis exists on EU, although many numerical experiments have been conducted on it. In this study, we analyze the EU of supervised learning in approximate Bayesian inference by focusing on its excess risk. F…
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…
How to efficiently explore in reinforcement learning is an open problem. Many exploration algorithms employ the epistemic uncertainty of their own value predictions -- for instance to compute an exploration bonus or upper confidence bound. Unfortunately the required uncertainty is difficult to estimate in general with function approximation. We propose epistemic value estimation (EVE): a recipe that is compatible with sequential decision making and with neural network function approximators. It equips agents with a tractable posterior over all their parameters from which epistemic value uncert…
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）
HybridFlow: Quantification of Aleatoric and Epistemic Uncertainty with a Single Hybrid Model
Department of Earth, Environment, and Planetary Sciences, Brown University（布朗大学地球、环境与行星科学系）；Data Science Institute, Brown University（布朗大学数据科学研究院）；Department of Computer Science, Brown University（布朗大学计算机科学系）
