Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat partitions of the sub-string set induced by the documents as Bernoulli random variables. The mean value of each random variable is an estimate of the classifier's precision when presented with a document inducing that partition. These means can be compared, using standard statistical tests, to a desired or expected classifier precision. A set of binary classifiers can be combined into a single, multi-label classifier by an application of the Dempster-Shafer theory of evidence. The utility of this approach is demonstrated with a benchmark problem.
The concept of trustworthy AI has gained widespread attention lately. One of the aspects relevant to trustworthy AI is robustness of ML models. In this study, we show how to probabilistically quantify robustness against naturally occurring distortions of input data for tree-based classifiers under the assumption that the natural distortions can be described by multivariate probability distributions that can be transformed to multivariate normal distributions. The idea is to extract the decision rules of a trained tree-based classifier, separate the feature space into non-overlapping regions an…
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, …
State-of-art deep neural networks (DNN) are vulnerable to attacks by adversarial examples: a carefully designed small perturbation to the input, that is imperceptible to human, can mislead DNN. To understand the root cause of adversarial examples, we quantify the probability of adversarial example existence for linear classifiers. Previous mathematical definition of adversarial examples only involves the overall perturbation amount, and we propose a more practical relevant definition of strong adversarial examples that separately limits the perturbation along the signal direction also. We show…
We propose two bounded comparison metrics that may be implemented to arbitrary dimensions in regression tasks. One quantifies the structure of uncertainty and the other quantifies the distribution of uncertainty. The structure metric assesses the similarity in shape and location of uncertainty with the true error, while the distribution metric quantifies the supported magnitudes between the two. We apply these metrics to Gaussian Processes (GPs), Ensemble Deep Neural Nets (DNNs), and Ensemble Deep Neural Operators (DNOs) on high-dimensional and nonlinear test cases. We find that comparing a mo…
Deep learning models achieve high predictive accuracy across a broad spectrum of tasks, but rigorously quantifying their predictive uncertainty remains challenging. Usable estimates of predictive uncertainty should (1) cover the true prediction targets with high probability, and (2) discriminate between high- and low-confidence prediction instances. Existing methods for uncertainty quantification are based predominantly on Bayesian neural networks; these may fall short of (1) and (2) -- i.e., Bayesian credible intervals do not guarantee frequentist coverage, and approximate posterior inference…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Graph Convolutional Network (GCN) has exhibited strong empirical performance in many real-world applications. The vast majority of existing works on GCN primarily focus on the accuracy while ignoring how confident or uncertain a GCN is with respect to its predictions. Despite being a cornerstone of trustworthy graph mining, uncertainty quantification on GCN has not been well studied and the scarce existing efforts either fail to provide deterministic quantification or have to change the training procedure of GCN by introducing additional parameters or architectures. In this paper, we propose t…
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…
The application of machine learning (ML) techniques in wireless communication domain has seen a tremendous growth over the years especially in the wireless sensing domain. However, the questions surrounding the ML model's inference reliability, and uncertainty associated with its predictions are never answered or communicated properly. This itself raises a lot of questions on the transparency of these ML systems. Developing ML systems with probabilistic modeling can solve this problem easily, where one can quantify uncertainty whether it is arising from the data (irreducible error or aleotoric…
Quantifying and managing uncertainties that occur when data-driven models such as those provided by AI and machine learning methods are applied is crucial. This whitepaper provides a brief motivation and first overview of the state of the art in identifying and quantifying sources of uncertainty for data-driven components as well as means for analyzing their impact.
Measurement of uncertainty of predictions from machine learning methods is important across scientific domains and applications. We present, to our knowledge, the first such technique that quantifies the uncertainty of predictions from a classifier and accounts for both the classifier's belief and performance. We prove that our method provides an accurate estimate of the probability that the outputs of two neural networks are correct by showing an expected calibration error of less than 0.2% on a binary classifier, and less than 3% on a semantic segmentation network with extreme class imbalanc…
University of California, Davis（加州大学戴维斯分校）；New York University（纽约大学）；University of California, Berkeley（加州大学伯克利分校）
With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that attaches an explicit uncertainty statement to the probabilities of classification using deep neural networks. Precisely, we view that the classification probabilities are sampled from an unknown distribution, and we propose to learn this distribution through the Dirichlet mixture that is flexible enough for approximating any continuous distribution on the simpl…
UT Dallas（德克萨斯大学达拉斯分校）；US Army Research Lab（美国陆军研究实验室）；Virginia Tech（弗吉尼亚理工学院暨州立大学）
Traditional deep neural nets (NNs) have shown the state-of-the-art performance in the task of classification in various applications. However, NNs have not considered any types of uncertainty associated with the class probabilities to minimize risk due to misclassification under uncertainty in real life. Unlike Bayesian neural nets indirectly infering uncertainty through weight uncertainties, evidential neural networks (ENNs) have been recently proposed to support explicit modeling of the uncertainty of class probabilities. It treats predictions of an NN as subjective opinions and learns the f…
Northeastern University（东北大学）；risQ Inc.（risQ公司）；Bay Area Environmental Research Institute（湾区环境研究所）；NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；NASA Advanced Supercomputing Division（美国国家航空航天局高级超级计算部）
Deep Learning (DL) methods have been transforming computer vision with innovative adaptations to other domains including climate change. For DL to pervade Science and Engineering (S&E) applications where risk management is a core component, well-characterized uncertainty estimates must accompany predictions. However, S&E observations and model-simulations often follow heavily skewed distributions and are not well modeled with DL approaches, since they usually optimize a Gaussian, or Euclidean, likelihood loss. Recent developments in Bayesian Deep Learning (BDL), which attempts to capture uncer…
Virginia Tech（弗吉尼亚理工大学）；U.S. Geological Survey（美国地质调查局）
To simultaneously address the rising need of expressing uncertainties in deep learning models along with producing model outputs which are consistent with the known scientific knowledge, we propose a novel physics-guided architecture (PGA) of neural networks in the context of lake temperature modeling where the physical constraints are hard coded in the neural network architecture. This allows us to integrate such models with state of the art uncertainty estimation approaches such as Monte Carlo (MC) Dropout without sacrificing the physical consistency of our results. We demonstrate the effect…
Delft University of Technology（代尔夫特理工大学）；University of Copenhagen（哥本哈根大学）；Leiden University Medical Center（莱顿大学医学中心）；University of Oslo（奥斯陆大学）
In various approaches to learning, notably in domain adaptation, active learning, learning under covariate shift, semi-supervised learning, learning with concept drift, and the like, one often wants to compare a baseline classifier to one or more advanced (or at least different) strategies. In this chapter, we basically argue that if such classifiers, in their respective training phases, optimize a so-called surrogate loss that it may also be valuable to compare the behavior of this loss on the test set, next to the regular classification error rate. It can provide us with an additional view o…
Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces challenges when inferring fields that have discrete representations of large dimension, and/or have prior distributions that are difficult to characterize mathematically. In this work we demonstrate how the approximate distribution learned by a deep generative adversarial network (GAN) may be used as a prior in a Bayesian update to address both these challenges. W…
SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；University of Oxford（牛津大学）
Virtual Diagnostic (VD) is a deep learning tool that can be used to predict a diagnostic output. VDs are especially useful in systems where measuring the output is invasive, limited, costly or runs the risk of damaging the output. Given a prediction, it is necessary to relay how reliable that prediction is. This is known as 'uncertainty quantification' of a prediction. In this paper, we use ensemble methods and quantile regression neural networks to explore different ways of creating and analyzing prediction's uncertainty on experimental data from the Linac Coherent Light Source at SLAC. We ai…
This paper aims to quantify uncertainty in traffic state estimation (TSE) using the generative adversarial network based physics-informed deep learning (PIDL). The uncertainty of the focus arises from fundamental diagrams, in other words, the mapping from traffic density to velocity. To quantify uncertainty for the TSE problem is to characterize the robustness of predicted traffic states. Since its inception, generative adversarial networks (GAN) have become a popular probabilistic machine learning framework. In this paper, we will inform the GAN based predictions using stochastic traffic flow…
Deep neural networks are increasingly being used for the analysis of medical images. However, most works neglect the uncertainty in the model's prediction. We propose an uncertainty-aware deep kernel learning model which permits the estimation of the uncertainty in the prediction by a pipeline of a Convolutional Neural Network and a sparse Gaussian Process. Furthermore, we adapt different pre-training methods to investigate their impacts on the proposed model. We apply our approach to Bone Age Prediction and Lesion Localization. In most cases, the proposed model shows better performance compar…
Cognizant（高知特）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Neural Networks (NNs) have been extensively used for a wide spectrum of real-world regression tasks, where the goal is to predict a numerical outcome such as revenue, effectiveness, or a quantitative result. In many such tasks, the point prediction is not enough: the uncertainty (i.e. risk or confidence) of that prediction must also be estimated. Standard NNs, which are most often used in such tasks, do not provide uncertainty information. Existing approaches address this issue by combining Bayesian models with NNs, but these models are hard to implement, more expensive to train, and usually d…
Classifiers are often tested on relatively small data sets, which should lead to uncertain performance metrics. Nevertheless, these metrics are usually taken at face value. We present an approach to quantify the uncertainty of classification performance metrics, based on a probability model of the confusion matrix. Application of our approach to classifiers from the scientific literature and a classification competition shows that uncertainties can be surprisingly large and limit performance evaluation. In fact, some published classifiers are likely to be misleading. The application of our app…
We present an analysis of predictive uncertainty based out-of-distribution detection for different approaches to estimate various models' epistemic uncertainty and contrast it with extreme value theory based open set recognition. While the former alone does not seem to be enough to overcome this challenge, we demonstrate that uncertainty goes hand in hand with the latter method. This seems to be particularly reflected in a generative model approach, where we show that posterior based open set recognition outperforms discriminative models and predictive uncertainty based outlier rejection, rais…
College of Aerospace Science and Engineering National University of Defense Technology（国防科技大学航空航天学院）；Defense Innovation Institute Chinese Academy of Military Science（中国人民解放军军事科学院国防创新研究院）
For the temperature field reconstruction (TFR), a complex image-to-image regression problem, the convolutional neural network (CNN) is a powerful surrogate model due to the convolutional layer's good image feature extraction ability. However, a lot of labeled data is needed to train CNN, and the common CNN can not quantify the aleatoric uncertainty caused by data noise. In actual engineering, the noiseless and labeled training data is hardly obtained for the TFR. To solve these two problems, this paper proposes a deep Monte Carlo quantile regression (Deep MC-QR) method for reconstructing the t…
Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry
Epistemic Intelligence & Computation Lab, College of Computing & Data Science, Nanyang Technological University, Singapore（新加坡南洋理工大学计算与数据科学学院）；CISPA Helmholtz Center for Information Security, Germany（德国亥姆霍兹信息安全中心）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Institute of Informatics, LMU Munich, Germany（德国慕尼黑机器学习中心）；Munich Center for Machine Learning, Germany（曼彻斯特人工智能基础研究中心）；Manchester Centre for AI Fundamentals, Manchester, United Kingdom Department of Computer Science, The University of Manchester, United Kingdom
Being uncertain when facing the unknown is key to intelligent decision making. However, machine learning algorithms lack reliable estimates about their predictive uncertainty. This leads to wrong and overly-confident decisions when encountering classes unseen during training. Despite the importance of equipping classifiers with uncertainty estimates ready for the real world, prior work has focused on small datasets and little or no class discrepancy between training and testing data. To close this gap, we introduce UIMNET: a realistic, ImageNet-scale test-bed to evaluate predictive uncertainty…
Technion – Israel Institute of Technology（以色列理工学院）
We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the classification problem at hand. We demonstrate that such techniques tend to introduce biased estimates for instances whose predictions are supposed to be highly confident. We argue that this deficiency is an artifact of the dynamics of training with SGD-like optimizers, and it has some properties similar to overfitting. Based on this observation, we develop an u…
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do not provide uncertainty on the obtained reconstruction. In this work, we develop a scalable, data-driven, knowledge-aided computational framework to quantify the model uncertainty via Bayesian neural networks. The approach builds on, and extends deep gradient descent, a recently developed greedy iterative training scheme, and recasts it within a probabilistic…
Accurate estimation of predictive uncertainty in modern neural networks is critical to achieve well calibrated predictions and detect out-of-distribution (OOD) inputs. The most promising approaches have been predominantly focused on improving model uncertainty (e.g. deep ensembles and Bayesian neural networks) and post-processing techniques for OOD detection (e.g. ODIN and Mahalanobis distance). However, there has been relatively little investigation into how the parametrization of the probabilities in discriminative classifiers affects the uncertainty estimates, and the dominant method, softm…
Knowing the uncertainty in a prediction is critical when making expensive investment decisions and when patient safety is paramount, but machine learning (ML) models in drug discovery typically provide only a single best estimate and ignore all sources of uncertainty. Predictions from these models may therefore be over-confident, which can put patients at risk and waste resources when compounds that are destined to fail are further developed. Probabilistic predictive models (PPMs) can incorporate uncertainty in both the data and model, and return a distribution of predicted values that represe…
Structure of Classifier Boundaries: Case Study for a Naive Bayes Classifier
Temple University, Department of Statistics, Operations, and Data Science（特拉华大学统计学、运营与数据科学系）；Fraunhofer USA Center Mid-Atlantic（弗劳恩霍夫美国中大西洋中心）；University of Maryland, Department of Computer Science（马里兰大学计算机科学系）；University of Pennsylvania, Computational Social Science Laboratory（宾夕法尼亚大学计算社会科学实验室）
Technion（以色列理工学院）；University of Southern California（南加州大学）
Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be overconfident. We begin to address this problem in the context of multi-class classification by developing a novel training algorithm producing models with more dependable uncertainty estimates, without sacrificing predictive power. The idea is to mitigate overconfidence by minimizing a loss function, inspired by advances in conformal inference, that quantifies mod…
Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Université Paul Sabatier（保尔·萨巴蒂埃大学）
We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do so, we analyze and propose two bounding schemes for uncertainties associated to random approximate features in low dimensional spaces. The proposed techniques are based on Random Fourier Features and the Nyström methods. The resulting formulations can be solved with efficient stochastic approximation techniques such as stochastic (sub)-gradient, stochastic p…
City, University of London（伦敦城市大学）；Bayes Business School（贝叶斯商学院）；University of Naples “Parthenope”（那不勒斯帕泰诺佩大学）
Classification models are very sensitive to data uncertainty, and finding robust classifiers that are less sensitive to data uncertainty has raised great interest in the machine learning literature. This paper aims to construct robust \emph{Support Vector Machine} classifiers under feature data uncertainty via two probabilistic arguments. The first classifier, \emph{Single Perturbation}, reduces the local effect of data uncertainty with respect to one given feature and acts as a local test that could confirm or refute the presence of significant data uncertainty for that particular feature. Th…
Microsoft（微软）；IIT Kanpur（印度理工学院坎普尔分校）；Oracle（甲骨文公司）；University of Bath（巴斯大学）
Understanding unsupervised domain adaptation has been an important task that has been well explored. However, the wide variety of methods have not analyzed the role of a classifier's performance in detail. In this paper, we thoroughly examine the role of a classifier in terms of matching source and target distributions. We specifically investigate the classifier ability by matching a) the distribution of features, b) probabilistic uncertainty for samples and c) certainty activation mappings. Our analysis suggests that using these three distributions does result in a consistently improved perfo…
