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 reducing the computational overhead. We apply our approach to large-scale visual tasks (i.e., semantic segmentation and depth regression) to demonstrate the advantages of our method compared to sampling-based approaches in terms of quality of the uncertainty estimates as well as of computational overhead.
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…
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）
Surrogate Modelling of Proton Dose with Monte Carlo Dropout Uncertainty Quantification
Institute for Mathematical Innovation University of Bath, Bath, UK（数学创新研究所 英国巴斯大学）；Department of Mathematical Sciences University of Bath, Bath, UK（数学科学系 英国巴斯大学）
Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification
Institute for Mathematical Innovation University of Bath, Bath, UK（数学创新研究所 英国巴斯大学）；Department of Mathematical Sciences University of Bath, Bath, UK（数学科学系 英国巴斯大学）
University of Oxford（牛津大学）；University of Cambridge（剑桥大学）
Optimization in the latent space of variational autoencoders is a promising approach to generate high-dimensional discrete objects that maximize an expensive black-box property (e.g., drug-likeness in molecular generation, function approximation with arithmetic expressions). However, existing methods lack robustness as they may decide to explore areas of the latent space for which no data was available during training and where the decoder can be unreliable, leading to the generation of unrealistic or invalid objects. We propose to leverage the epistemic uncertainty of the decoder to guide the…
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…
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）
The Plackett-Luce (PL) model is ubiquitous in learning-to-rank (LTR) because it provides a useful and intuitive probabilistic model for sampling ranked lists. Counterfactual offline evaluation and optimization of ranking metrics are pivotal for using LTR methods in production. When adopting the PL model as a ranking policy, both tasks require the computation of expectations with respect to the model. These are usually approximated via Monte-Carlo (MC) sampling, since the combinatorial scaling in the number of items to be ranked makes their analytical computation intractable. Despite recent adv…
Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization
Bosch Corporate Research（博世公司研究中心）；Technical University Darmstadt（达姆施塔特工业大学）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；Centre for Cognitive Science（认知科学中心）
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…
We consider the computation of the permanent of a binary n by n matrix. It is well- known that the exact computation is a #P complete problem. A variety of Markov chain Monte Carlo (MCMC) computational algorithms have been introduced in the literature whose cost, in order to achieve a given level of accuracy, is O(n^7 log^4(n)). These algorithms use a particular collection of probability distributions, the `ideal' of which, (in some sense) are not known and need to be approximated. In this paper we propose an adaptive sequential Monte Carlo (SMC) algorithm that can both estimate the permanent …
Variational LSTM with Augmented Inputs: Nonlinear Response History Metamodeling with Aleatoric and Epistemic Uncertainty
Department of Civil, Environmental, and Construction Engineering, Texas Tech University（德克萨斯理工大学土木、环境与建筑工程系）；Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute（伦斯勒理工学院土木与环境工程系）；National Wind Institute, Texas Tech University（德克萨斯理工大学国家风能研究所）
Efficient Epistemic Uncertainty Estimation for Large Language Models via Knowledge Distillation
Graduate School of Data Science, Seoul National University（首尔国立大学数据科学研究生院）；Department of Rural Systems Engineering, Seoul National University（首尔国立大学农村系统工程系）；Department of Aerospace Engineering, Seoul National University（首尔国立大学航空航天工程系）；Department of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology（全州科学科技研究院电子工程与计算机科学系）
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）
Instituto de Ingenieria de Aragon (I3A)（阿拉贡工程研究所）；Universidad de Zaragoza（萨拉戈萨大学）
Affordances are a fundamental concept in robotics since they relate available actions for an agent depending on its sensory-motor capabilities and the environment. We present a novel Bayesian deep network to detect affordances in images, at the same time that we quantify the distribution of the aleatoric and epistemic variance at the spatial level. We adapt the Mask-RCNN architecture to learn a probabilistic representation using Monte Carlo dropout. Our results outperform the state-of-the-art of deterministic networks. We attribute this improvement to a better probabilistic feature space repre…
For small training set sizes $P$, the generalization error of wide neural networks is well-approximated by the error of an infinite width neural network (NN), either in the kernel or mean-field/feature-learning regime. However, after a critical sample size $P^*$, we empirically find the finite-width network generalization becomes worse than that of the infinite width network. In this work, we empirically study the transition from infinite-width behavior to this variance limited regime as a function of sample size $P$ and network width $N$. We find that finite-size effects can become relevant f…
One step closer to unbiased aleatoric uncertainty estimation
Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；University of California（加利福尼亚大学）
Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's predictions is interpreted as its epistemic uncertainty. The appeal of ensembling stems from being a collection of regular NNs - this makes them both scalable and easily implementable. They have achieved strong empirical results in recent years, often presented as a practical alternative to more costly Bayesian NNs (BNNs). The departure from Bayesian methodol…
Argonne National Laboratory（阿贡国家实验室）；Université Paris-Saclay（巴黎萨克雷大学）
Deep neural networks are powerful predictors for a variety of tasks. However, they do not capture uncertainty directly. Using neural network ensembles to quantify uncertainty is competitive with approaches based on Bayesian neural networks while benefiting from better computational scalability. However, building ensembles of neural networks is a challenging task because, in addition to choosing the right neural architecture or hyperparameters for each member of the ensemble, there is an added cost of training each model. We propose AutoDEUQ, an automated approach for generating an ensemble of …
Fully Heteroscedastic Count Regression with Deep Double Poisson Networks
Brigham Young University, Department of Computer Science（Brigham Young 大学计算机科学系）；Arizona State University, School of Computing and Augmented Intelligence（亚利桑那州立大学计算与增强智能学院）；Ohio State University, Department of Marketing（俄亥俄州立大学市场营销系）
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；Université de Montréal（蒙特利尔大学）
The impressive performance of deep neural networks (DNNs) has immensely strengthened the line of research that aims at theoretically analyzing their effectiveness. This has incited research on the reaction of DNNs to noisy input, namely developing adversarial input attacks and strategies that lead to robust DNNs to these attacks. To that end, in this paper, we derive exact analytic expressions for the first and second moments (mean and variance) of a small piecewise linear (PL) network (Affine, ReLU, Affine) subject to Gaussian input. In particular, we generalize the second-moment expression o…
Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems
School of Electrical and Computer Engineering, Purdue University（普渡大学电气与计算机工程学院）；School of Electrical and Computer Engineering, University of Southern California（南加州大学电气与计算机工程学院）；School of Biomedical Engineering, Purdue University（普渡大学生物医学工程学院）
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Arizona State University（亚利桑那州立大学）
We are interested in estimating the uncertainties of deep neural networks, which play an important role in many scientific and engineering problems. In this paper, we present a striking new finding that an ensemble of neural networks with the same weight initialization, trained on datasets that are shifted by a constant bias gives rise to slightly inconsistent trained models, where the differences in predictions are a strong indicator of epistemic uncertainties. Using the neural tangent kernel (NTK), we demonstrate that this phenomena occurs in part because the NTK is not shift-invariant. Sinc…
University of Michigan（密歇根大学）；DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室）；BI Norwegian Business School（BI挪威商学院）；University of Brescia（布雷西亚大学）
In second-order uncertain Bayesian networks, the conditional probabilities are only known within distributions, i.e., probabilities over probabilities. The delta-method has been applied to extend exact first-order inference methods to propagate both means and variances through sum-product networks derived from Bayesian networks, thereby characterizing epistemic uncertainty, or the uncertainty in the model itself. Alternatively, second-order belief propagation has been demonstrated for polytrees but not for general directed acyclic graph structures. In this work, we extend Loopy Belief Propagat…
