We propose a fast, non-Bayesian method for producing uncertainty scores in the output of pre-trained deep neural networks (DNNs) using a data-driven interval propagating network. This interval neural network (INN) has interval valued parameters and propagates its input using interval arithmetic. The INN produces sensible lower and upper bounds encompassing the ground truth. We provide theoretical justification for the validity of these bounds. Furthermore, its asymmetric uncertainty scores offer additional, directional information beyond what Gaussian-based, symmetric variance estimation can provide. We find that noise in the data is adequately captured by the intervals produced with our method. In numerical experiments on an image reconstruction task, we demonstrate the practical utility of INNs as a proxy for the prediction error in comparison to two state-of-the-art uncertainty quantification methods. In summary, INNs produce fast, theoretically justified uncertainty scores for DNNs that are easy to interpret, come with added information and pose as improved error proxies - features that may prove useful in advancing the usability of DNNs especially in sensitive applications such as health care.
MIT（麻省理工学院）；University of California, Berkeley（加州大学伯克利分校）；Technion—Israel Institute of Technology（以色列理工学院）
Meaningful uncertainty quantification in computer vision requires reasoning about semantic information -- say, the hair color of the person in a photo or the location of a car on the street. To this end, recent breakthroughs in generative modeling allow us to represent semantic information in disentangled latent spaces, but providing uncertainties on the semantic latent variables has remained challenging. In this work, we provide principled uncertainty intervals that are guaranteed to contain the true semantic factors for any underlying generative model. The method does the following: (1) it u…
Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to a specific operating point, making evaluation and comparison across different studies difficult. Our work leverages: (1) the concept of operating characteristics curves and (2) the notion of a gain over a simple reference, to derive a novel operating point agnostic assessment methodology for prediction intervals. The paper describes the corresponding algorithm, provides a theoretical …
University of Waterloo（滑铁卢大学）；University of Toronto（多伦多大学）
We propose a network architecture capable of reliably estimating uncertainty of regression based predictions without sacrificing accuracy. The current state-of-the-art uncertainty algorithms either fall short of achieving prediction accuracy comparable to the mean square error optimization or underestimate the variance of network predictions. We propose a decoupled network architecture that is capable of accomplishing both at the same time. We achieve this by breaking down the learning of prediction and prediction interval (PI) estimations into a two-stage training process. We use a custom los…
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）；IBM Research AI（IBM研究院人工智能部门）
With rapid adoption of deep learning in critical applications, the question of when and how much to trust these models often arises, which drives the need to quantify the inherent uncertainties. While identifying all sources that account for the stochasticity of models is challenging, it is common to augment predictions with confidence intervals to convey the expected variations in a model's behavior. We require prediction intervals to be well-calibrated, reflect the true uncertainties, and to be sharp. However, existing techniques for obtaining prediction intervals are known to produce unsati…
Uncertainty-Aware Multimodal Learning via Conformal Shapley Intervals
Department of Statistics and Data Science, UCLA（统计与数据科学系， UCLA）；Merck & Co（默克公司）；Department of Biostatistics, UCLA（生物统计学系， UCLA）；Departments of Statistics and Data Science, and of Biostatistics, UCLA（统计与数据科学系以及生物统计学系， UCLA）
Deep neural networks (DNNs) are becoming more prevalent in important safety-critical 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 focus…
Uncertainty quantification is crucial to assess prediction quality of a machine learning model. In the case of Extreme Learning Machines (ELM), most methods proposed in the literature make strong assumptions on the data, ignore the randomness of input weights or neglect the bias contribution in confidence interval estimations. This paper presents novel estimations that overcome these constraints and improve the understanding of ELM variability. Analytical derivations are provided under general assumptions, supporting the identification and the interpretation of the contribution of different va…
Direct Interval Propagation Methods using Neural-Network Surrogates for Uncertainty Quantification in Physical Systems Surrogate Model
LMSD, Department of Mechanical Engineering, KU Leuven（KU莱顿机械工程系LMSD）；RAM, Department of Mechanical Engineering, KU Leuven（KU莱顿机械工程系RAM）；DistriNet, Department of Computer Science, KU Leuven（KU莱顿计算机科学系DistriNet）；Visual Artificial Intelligence Laboratory, Oxford Brookes University（奥克斯福德布鲁克斯大学视觉人工智能实验室）
McGill University（麦吉尔大学）；University of Michigan（密歇根大学）
While the accuracy of modern deep learning models has significantly improved in recent years, the ability of these models to generate uncertainty estimates has not progressed to the same degree. Uncertainty methods are designed to provide an estimate of class probabilities when predicting class assignment. While there are a number of proposed methods for estimating uncertainty, they all suffer from a lack of calibration: predicted probabilities can be off from empirical ones by a few percent or more. By restricting the scope of our predictions to only the probability of Top-1 error, we can dec…
Explainable Uncertainty Quantification for Wastewater Treatment Energy Prediction via Interval Type-2 Neuro-Fuzzy System
Jheronimus Academy of Data Science, Eindhoven University of Technology, Eindhoven, The Netherlands（杰罗尼穆斯数据科学学院，埃因霍温理工大学，埃因霍温，荷兰）；Haskoning, Amersfoort, The Netherlands（哈索宁，阿默斯福尔特，荷兰）；School of Industrial Engineering, Eindhoven University of Technology（工业工程学院，埃因霍温理工大学）
Unveil Sources of Uncertainty: Feature Contribution to Conformal Prediction Intervals
Département de Mathématiques, Université du Québec à Montréal（魁北克大学蒙特利尔分校数学系）；Institut Intelligence et Données, Université Laval（拉瓦尔大学智能与数据研究所）；CNRS - Université de Montréal（法国国家科学研究中心-蒙特利尔大学）；CRM – CNRS Aix Marseille Univ, CNRS, AMSE, Marseille, France（法国国家科学研究中心-阿维尼昂大学）
CEA（法国原子能和替代能源委员会）；Inria（法国国家信息与自动化研究所）；AIM；CNRS（法国国家科学研究中心）；Université Paris-Saclay（巴黎-萨克雷大学）；Université Paris Diderot（巴黎狄德罗大学）；Sorbonne Paris Cité（索邦巴黎西岱大学）
Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework forsolving inverse problems, in which we limit the use of deep neural networks tolearning a prior distribution on the signals to recover. We adopt recent denoisingscore matching techniques to learn this prior from data, and subsequently use it aspart of an annealed Hamiltonian Monte-Carlo scheme to sample the full posteriorof image inverse problems. We apply this fra…
Better Uncertainty Calibration via Proper Scores for Classification and Beyond
German Cancer Research Center (DKFZ)（德国癌症研究中心）；German Cancer Consortium (DKTK)（德国癌症联盟）；Goethe University Frankfurt（法兰克福大学）；Frankfurt Cancer Institute（法兰克福癌症研究所）
Norwegian University of Science and Technology (NTNU)（挪威科技大学）
Prediction intervals are a machine- and human-interpretable way to represent predictive uncertainty in a regression analysis. In this paper, we present a method for generating prediction intervals along with point estimates from an ensemble of neural networks. We propose a multi-objective loss function fusing quality measures related to prediction intervals and point estimates, and a penalty function, which enforces semantic integrity of the results and stabilizes the training process of the neural networks. The ensembled prediction intervals are aggregated as a split normal mixture accounting…
We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion -- the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage estimation algorithm proposed by Cai et al. (2019), we characterize the distribution of this nonconvex estimator down to fine scales. This distributional theory in turn allows one to construct valid and short confidence intervals for both the unseen tensor entries and the unknown tensor factors. The proposed inferential procedure enjoys several important features: (1) it…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）
Accounting for the uncertainty in the predictions of modern neural networks is a challenging and important task in many domains. Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure (e.g., Bayesian neural networks) or dramatically increase the computational cost of predictions such as approaches based on ensembling. This work proposes a new algorithm that can be applied to a given trained neural network and produces approximate prediction intervals. The method is based on the classical delta method in statistics but achieves computation…
Hybrid Gaussian Process Regression with Temporal Feature Extraction for Partially Interpretable Remaining Useful Life Interval Prediction in Aeroengine Prognostics
UC San Diego（加州大学圣地亚哥分校）；University of Washington（华盛顿大学）；Northeastern University（东北大学）
Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to generate probabilistic forecasts with confidence intervals is critical to risk assessment and decision making. Hence, a systematic study of uncertainty quantification (UQ) methods for spatiotemporal forecasting is missing in the community. In this paper, we describe two types of spatiotemporal forecasting problems: regular grid-based and graph-based. Then we analyz…
Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling
Cornell University（康奈尔大学）；Ecole Polytechnique Federale de Lausanne (EPFL)（洛桑联邦理工学院）；Sandia National Laboratories（桑迪亚国家实验室）；University of Southern California（南加州大学）；Pasteur Labs（巴斯德实验室）
Uncertainty Quantification for Regression: A Unified Framework based on kernel scores
LMU Munich（慕尼黑莱茵恩大学）；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-特罗姆瑟大学）；German Research Center for Artificial Intelligence (DFKI, DSA)（德国人工智能研究中心）
The Distributional Uncertainty of the SHAP score in Explainable Machine Learning
Instituto de Ciencias de la Computación, UBA-CONICET（阿根廷计算机科学与技术研究所（布宜诺斯艾利斯大学-阿根廷国家科学与技术研究理事会联合机构））；Department of Computer Science, Universidad de Buenos Aires（布宜诺斯艾利斯大学计算机科学系）；Carleton Univ.（卡尔顿大学）；IMFD（智利数学物理研究所）；Universidad San Sebastián（圣塞瓦斯蒂安大学）；Department of Computer Science, University of Sheffield（谢菲尔德大学计算机科学系）；Artificial Intelligence Research Institute (IIIA-CSIC)（西班牙国家研究委员会人工智能研究所）；Universidad Católica de Chile（智利天主教大学）；CENIA Chile（智利国家环境技术中心）
Towards Trustworthy Vital Sign Forecasting: Leveraging Uncertainty for Prediction Intervals
College of Computing（计算学院）；Data Science Nanyang Technological University（南洋理工大学数据科学系）；Nanyang Technological University（南洋理工大学）；A*STAR Centre for Frontier AI Research（前沿人工智能研究中心）；School of Computing（计算学院）；University of Utah（犹他大学）；Swee Hock School of Public Health（公共卫生学院）；National University of Singapore（新加坡国立大学）；Lee Kong Chian School of Medicine（李科钦医学院）
Deep learning has achieved impressive performance on many tasks in recent years. However, it has been found that it is still not enough for deep neural networks to provide only point estimates. For high-risk tasks, we need to assess the reliability of the model predictions. This requires us to quantify the uncertainty of model prediction and construct prediction intervals. In this paper, We explore the uncertainty in deep learning to construct the prediction intervals. In general, We comprehensively consider two categories of uncertainties: aleatory uncertainty and epistemic uncertainty. We de…
Effective decision making requires understanding the uncertainty inherent in a prediction. In regression, this uncertainty can be estimated by a variety of methods; however, many of these methods are laborious to tune, generate overconfident uncertainty intervals, or lack sharpness (give imprecise intervals). We address these challenges by proposing a novel method to capture predictive distributions in regression by defining two neural networks with two distinct loss functions. Specifically, one network approximates the cumulative distribution function, and the second network approximates its …
Many traffic prediction applications rely on uncertainty estimates instead of the mean prediction. Statistical traffic prediction literature has a complete subfield devoted to uncertainty modelling, but recent deep learning traffic prediction models either lack this feature or make specific assumptions that restrict its practicality. We propose Quantile Graph Wavenet, a Spatio-Temporal neural network that is trained to estimate a density given the measurements of previous timesteps, conditioned on a quantile. Our method of density estimation is fully parameterised by our neural network and doe…
Nagoya Institute of Technology（名古屋工业大学）；University of Tsukuba（筑波大学）；Japan Science and Technology Agency（日本科学技术振兴机构）；RIKEN（理化学研究所）；National Institute for Materials Science（国立材料科学研究所）
The problem of machine learning with missing values is common in many areas. A simple approach is to first construct a dataset without missing values simply by discarding instances with missing entries or by imputing a fixed value for each missing entry, and then train a prediction model with the new dataset. A drawback of this naive approach is that the uncertainty in the missing entries is not properly incorporated in the prediction. In order to evaluate prediction uncertainty, the multiple imputation (MI) approach has been studied, but the performance of MI is sensitive to the choice of the…
Certainty in Uncertainty: Reasoning over Uncertain Knowledge Graphs with Statistical Guarantees
University of Stuttgart（斯图加特大学）；Bosch Center for AI（博世人工智能中心）；The University of Manchester（曼彻斯特大学）；University of Oslo（奥斯陆大学）；University of Southampton（南安普顿大学）
The transductive inference is an effective technique in the few-shot learning task, where query sets update prototypes to improve themselves. However, these methods optimize the model by considering only the classification scores of the query instances as confidence while ignoring the uncertainty of these classification scores. In this paper, we propose a novel method called Uncertainty-Based Network, which models the uncertainty of classification results with the help of mutual information. Specifically, we first data augment and classify the query instance and calculate the mutual informatio…
Most of statistics and AI draw insights through modelling discord or variance between sources of information (i.e., inter-source uncertainty). Increasingly, however, research is focusing upon uncertainty arising at the level of individual measurements (i.e., within- or intra-source), such as for a given sensor output or human response. Here, adopting intervals rather than numbers as the fundamental data-type provides an efficient, powerful, yet challenging way forward -- offering systematic capture of uncertainty-at-source, increasing informational capacity, and ultimately potential for insigh…
University College London（伦敦大学学院）；King’s College London（伦敦国王学院）
Counting is a fundamental task in biomedical imaging and count is an important biomarker in a number of conditions. Estimating the uncertainty in the measurement is thus vital to making definite, informed conclusions. In this paper, we first compare a range of existing methods to perform counting in medical imaging and suggest ways of deriving predictive intervals from these. We then propose and test a method for calculating intervals as an output of a multi-task network. These predictive intervals are optimised to be as narrow as possible, while also enclosing a desired percentage of the data…
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）
