We propose a method for training a deterministic deep model that can find and reject out of distribution data points at test time with a single forward pass. Our approach, deterministic uncertainty quantification (DUQ), builds upon ideas of RBF networks. We scale training in these with a novel loss function and centroid updating scheme and match the accuracy of softmax models. By enforcing detectability of changes in the input using a gradient penalty, we are able to reliably detect out of distribution data. Our uncertainty quantification scales well to large datasets, and using a single model, we improve upon or match Deep Ensembles in out of distribution detection on notable difficult dataset pairs such as FashionMNIST vs. MNIST, and CIFAR-10 vs. SVHN.
University of Oxford（牛津大学）；OATML, Department of Computer Science, University of Oxford（牛津大学计算机科学系OATML）；Torr Vision Group, Department of Engineering Science, University of Oxford（牛津大学工程科学系Torr视觉组）
Reliable uncertainty from deterministic single-forward pass models is sought after because conventional methods of uncertainty quantification are computationally expensive. We take two complex single-forward-pass uncertainty approaches, DUQ and SNGP, and examine whether they mainly rely on a well-regularized feature space. Crucially, without using their more complex methods for estimating uncertainty, a single softmax neural net with such a feature-space, achieved via residual connections and spectral normalization, *outperforms* DUQ and SNGP's epistemic uncertainty predictions using simple Ga…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Technology Innovation Institute（技术创新研究所）；HSE University（高等经济大学）；Nuro, Inc.（Nuro公司）；Lomonosov Moscow State University（罗蒙诺索夫莫斯科国立大学）；AIRI；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
This paper proposes a fast and scalable method for uncertainty quantification of machine learning models' predictions. First, we show the principled way to measure the uncertainty of predictions for a classifier based on Nadaraya-Watson's nonparametric estimate of the conditional label distribution. Importantly, the proposed approach allows to disentangle explicitly aleatoric and epistemic uncertainties. The resulting method works directly in the feature space. However, one can apply it to any neural network by considering an embedding of the data induced by the network. We demonstrate the str…
Comparison of Deterministic and Probabilistic Machine Learning Algorithms for Precise Dimensional Control and Uncertainty Quantification in Additive Manufacturing
Center for Nanoscale Materials, Argonne National Laboratory（阿贡国家实验室纳米尺度材料中心）；Department of Mechanical and Industrial Engineering, University of Illinois, Chicago（伊利诺伊大学芝加哥分校机械与工业工程系）；Shell International Exploration and Production Inc.（壳牌国际勘探与生产公司）
Accurate and efficient uncertainty estimation is crucial to build reliable Machine Learning (ML) models capable to provide calibrated uncertainty estimates, generalize and detect Out-Of-Distribution (OOD) datasets. To this end, Deterministic Uncertainty Methods (DUMs) is a promising model family capable to perform uncertainty estimation in a single forward pass. This work investigates important design choices in DUMs: (1) we show that training schemes decoupling the core architecture and the uncertainty head schemes can significantly improve uncertainty performances. (2) we demonstrate that th…
Uncertainty estimation is a key component in any deployed machine learning system. One way to evaluate uncertainty estimation is using "out-of-distribution" (OoD) detection, that is, distinguishing between the training data distribution and an unseen different data distribution using uncertainty. In this work, we show that current feature density based uncertainty estimators cannot perform well consistently across different OoD detection settings. To solve this, we propose to decompose the learned representations and integrate the uncertainties estimated on them separately. Through experiments…
Bosch Center for Artificial Intelligence（博世人工智能中心）；University of Southern Denmark（南丹麦大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been remained unexplored so far. We report the empirical finding that obtaining well-calibrated uncertainty estimations from NSDEs is computationally prohibitive. As a remedy, we develop a computationally affordable deterministic scheme which accurately approximates the transition kernel, when dynamics is governed by a NSDE. Our method introduces a bidimensional m…
We present a new method for uncertainty estimation and out-of-distribution detection in neural networks with softmax output. We extend softmax layer with an additional constant input. The corresponding additional output is able to represent the uncertainty of the network. The proposed method requires neither additional parameters nor multiple forward passes nor input preprocessing nor out-of-distribution datasets. We show that our method performs comparably to more computationally expensive methods and outperforms baselines on our experiments from image recognition and sentiment analysis domai…
Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different submodels, which leads to slow uncertainty estimation at inference time. Recent works address this drawback by directly predicting parameters of prior distributions over the probability predictions with a neural network. While this approach has demonstrated accurate uncertainty estimation, it requires defining arbitrary target parameters for in-distribution …
We propose a novel method to capture data points near decision boundary in neural network that are often referred to a specific type of uncertainty. In our approach, we sought to perform uncertainty estimation based on the idea of adversarial attack method. In this paper, uncertainty estimates are derived from the input perturbations, unlike previous studies that provide perturbations on the model's parameters as in Bayesian approach. We are able to produce uncertainty with couple of perturbations on the inputs. Interestingly, we apply the proposed method to datasets derived from blockchain. W…
Mila（米拉研究所）；McGill University（麦吉尔大学）；Université de Montréal（蒙特利尔大学）；UBC Okanagan（不列颠哥伦比亚大学奥卡那根分校）
Distribution shift is an important concern in deep image classification, produced either by corruption of the source images, or a complete change, with the solution involving domain adaptation. While the primary goal is to improve accuracy under distribution shift, an important secondary goal is uncertainty estimation: evaluating the probability that the prediction of a model is correct. While improving accuracy is hard, uncertainty estimation turns out to be frustratingly easy. Prior works have appended uncertainty estimation into the model and training paradigm in various ways. Instead, we s…
Southern University of Science and Technology（南方科技大学）；Chongqing Jiaotong University（重庆交通大学）；Tsinghua University（清华大学）；China Automotive Engineering Research Institute（中国汽车工程研究院股份有限公司）；Dalian University of Technology（大连理工大学）；Zhejiang University（浙江大学）
Variational autoencoders (VAEs) are influential generative models with rich representation capabilities from the deep neural network architecture and Bayesian method. However, VAE models have a weakness that assign a higher likelihood to out-of-distribution (OOD) inputs than in-distribution (ID) inputs. To address this problem, a reliable uncertainty estimation is considered to be critical for in-depth understanding of OOD inputs. In this study, we propose an improved noise contrastive prior (INCP) to be able to integrate into the encoder of VAEs, called INCPVAE. INCP is scalable, trainable an…
Skolkovo Institute of Science and Technology (Skoltech)（斯科尔科沃科技学院（Skoltech））；Yandex（Yandex（扬德克斯））
Uncertainty estimation for machine learning models is of high importance in many scenarios such as constructing the confidence intervals for model predictions and detection of out-of-distribution or adversarially generated points. In this work, we show that modifying the sampling distributions for dropout layers in neural networks improves the quality of uncertainty estimation. Our main idea consists of two main steps: computing data-driven correlations between neurons and generating samples, which include maximally diverse neurons. In a series of experiments on simulated and real-world data, …
In this work we aim to obtain computationally-efficient uncertainty estimates with deep networks. For this, we propose a modified knowledge distillation procedure that achieves state-of-the-art uncertainty estimates both for in and out-of-distribution samples. Our contributions include a) demonstrating and adapting to distillation's regularization effect b) proposing a novel target teacher distribution c) a simple augmentation procedure to improve out-of-distribution uncertainty estimates d) shedding light on the distillation procedure through comprehensive set of experiments.
Massachusetts Institute of Technology（麻省理工学院）；Raytheon BBN Technologies（雷神BBN技术公司）
While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function for regression uncertainty estimation based on the Bayesian Validation Metric (BVM) framework while using ensemble learning. The proposed loss reproduces maximum likelihood estimation in the limiting case. A series of experiments on in-distribution data show that the proposed method is competitive with existing state-of-the-art methods. Experiments on out-of…
While deep neural networks provide good performance for a range of challenging tasks, calibration and uncertainty estimation remain major challenges, especially under distribution shift. In this paper, we propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation, calibration, and out-of-distribution robustness with deep networks. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principl…
Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still require prohibitive computational costs. We propose a family of algorithms which split the classification task into two stages: representation learning and uncertainty estimation. We compare four specific instances, where uncertainty estimation is performed via either an ensemble of Stochastic Gradient Descent or Stochastic Gradient Langevin Dynamics snapshots, an…
ENSTA Paris, Institut polytechnique de Paris（巴黎高等先进技术学院，巴黎理工学院）；Paris-Saclay University（巴黎萨克雷大学）；Aix Marseille University（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）
Predictive uncertainty estimation is essential for deploying Deep Neural Networks in real-world autonomous systems. However, most successful approaches are computationally intensive. In this work, we attempt to address these challenges in the context of autonomous driving perception tasks. Recently proposed Deterministic Uncertainty Methods (DUM) can only partially meet such requirements as their scalability to complex computer vision tasks is not obvious. In this work we advance a scalable and effective DUM for high-resolution semantic segmentation, that relaxes the Lipschitz constraint typic…
Machine learning classifiers are probabilistic in nature, and thus inevitably involve uncertainty. Predicting the probability of a specific input to be correct is called uncertainty (or confidence) estimation and is crucial for risk management. Post-hoc model calibrations can improve models' uncertainty estimations without the need for retraining, and without changing the model. Our work puts forward a geometric-based approach for uncertainty estimation. Roughly speaking, we use the geometric distance of the current input from the existing training inputs as a signal for estimating uncertainty…
Calibrated estimates of uncertainty are critical for many real-world computer vision applications of deep learning. While there are several widely-used uncertainty estimation methods, dropout inference stands out for its simplicity and efficacy. This technique, however, requires multiple forward passes through the network during inference and therefore can be too resource-intensive to be deployed in real-time applications. We propose a simple, easy-to-optimize distillation method for learning the conditional predictive distribution of a pre-trained dropout model for fast, sample-free uncertain…
Cornell University（康奈尔大学）；Cornell Tech（康奈尔理工学院）；Shutterstock（Shutterstock公司）；Rochester Institute of Technology（罗切斯特理工学院）
For many applications it is critical to know the uncertainty of a neural network's predictions. While a variety of neural network parameter estimation methods have been proposed for uncertainty estimation, they have not been rigorously compared across uncertainty measures. We assess four of these parameter estimation methods to calibrate uncertainty estimation using four different uncertainty measures: entropy, mutual information, aleatoric uncertainty and epistemic uncertainty. We evaluate the calibration of these parameter estimation methods using expected calibration error. Additionally, we…
Institute of Computer Graphics and Vision（计算机图形与视觉研究所）；Graz University of Technology（格拉茨理工大学）；School of Computer Science（计算机科学学院）；University of Auckland（奥克兰大学）
Additionally to the extensive use in clinical medicine, biological age (BA) in legal medicine is used to assess unknown chronological age (CA) in applications where identification documents are not available. Automatic methods for age estimation proposed in the literature are predicting point estimates, which can be misleading without the quantification of predictive uncertainty. In our multi-factorial age estimation method from MRI data, we used the Variational Inference approach to estimate the uncertainty of a Bayesian CNN model. Distinguishing model uncertainty from data uncertainty, we in…
The article focuses on determining the predictive uncertainty of a model on the example of atrial fibrillation detection problem by a single-lead ECG signal. To this end, the model predicts parameters of the beta distribution over class probabilities instead of these probabilities themselves. It was shown that the described approach allows to detect atypical recordings and significantly improve the quality of the algorithm on confident predictions.
Deep neural networks (DNNs) have proven to be powerful predictors and are widely used for various tasks. Credible uncertainty estimation of their predictions, however, is crucial for their deployment in many risk-sensitive applications. In this paper we present a novel and simple attack, which unlike adversarial attacks, does not cause incorrect predictions but instead cripples the network's capacity for uncertainty estimation. The result is that after the attack, the DNN is more confident of its incorrect predictions than about its correct ones without having its accuracy reduced. We present …
Fraunhofer IAIS（弗劳恩霍夫智能分析与信息系统研究所）；Fraunhofer Center for Machine Learning（弗劳恩霍夫机器学习中心）；Volkswagen AG（大众汽车集团）；University of Bonn（波恩大学）
Uncertainty estimation bears the potential to make deep learning (DL) systems more reliable. Standard techniques for uncertainty estimation, however, come along with specific combinations of strengths and weaknesses, e.g., with respect to estimation quality, generalization abilities and computational complexity. To actually harness the potential of uncertainty quantification, estimators are required whose properties closely match the requirements of a given use case. In this work, we propose a framework that, firstly, structures and shapes these requirements, secondly, guides the selection of …
Uncertainty estimation is essential to make neural networks trustworthy in real-world applications. Extensive research efforts have been made to quantify and reduce predictive uncertainty. However, most existing works are designed for unimodal data, whereas multi-view uncertainty estimation has not been sufficiently investigated. Therefore, we propose a new multi-view classification framework for better uncertainty estimation and out-of-domain sample detection, where we associate each view with an uncertainty-aware classifier and combine the predictions of all the views in a principled way. Th…
In many applications with real-world consequences, it is crucial to develop reliable uncertainty estimation for the predictions made by the AI decision systems. Targeting at the goal of estimating uncertainty, various deep neural network (DNN) based uncertainty estimation algorithms have been proposed. However, the robustness of the uncertainty returned by these algorithms has not been systematically explored. In this work, to raise the awareness of the research community on robust uncertainty estimation, we show that state-of-the-art uncertainty estimation algorithms could fail catastrophical…
Due to the comprehensive nature of this paper, it has been updated and split into two separate papers: "A Framework For Benchmarking Class-out-of-distribution Detection And Its Application To ImageNet" and "What Can We Learn From The Selective Prediction And Uncertainty Estimation Performance Of 523 Imagenet Classifiers". We recommend reading them instead. Deep neural networks must be equipped with an uncertainty estimation mechanism when deployed for risk-sensitive tasks. This paper studies the relationship between deep architectures and their training regimes with their corresponding selecti…
School of Computing, the Australian National University（澳大利亚国立大学计算学院）；School of Electronics and Information, Northwestern Polytechnical University（西北工业大学电子信息学院）；CS, Nankai University（南开大学计算机学院）；CSIRO（澳大利亚联邦科学与工业研究组织）；Monash University（莫纳什大学）
Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the weights, which leads to deterministic predictions during testing. In this way, a specific weights set is estimated while ignoring any uncertainty that may occur in the proper weight space. The latter introduces randomness into the framework, either by assuming a prior distribution over model parameters (i.e. Bayesian Neural Networks) or including latent variable…
In computational histopathology algorithms now outperform humans on a range of tasks, but to date none are employed for automated diagnoses in the clinic. Before algorithms can be involved in such high-stakes decisions they need to "know when they don't know", i.e., they need to estimate their predictive uncertainty. This allows them to defer potentially erroneous predictions to a human pathologist, thus increasing their safety. Here, we evaluate the predictive performance and calibration of several uncertainty estimation methods on clinical histopathology data. We show that a distance-aware u…
Bonn-Rhein-Sieg University of Applied Sciences（波恩-莱茵-锡格应用技术大学）；German Aerospace Center (DLR)（德国航空航天中心）；University of Luxembourg（卢森堡大学）
We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect estimation of uncertainty. We propose the use of a heavy-tailed distribution (Laplace distribution) to improve the robustness to outliers. This property is evaluated using standard regression benchmarks and on a high-dimensional regression task of monocular depth estimation, both containing outliers. In particular, heavy-tailed distribution based maximum likelihoo…
When deployed for risk-sensitive tasks, deep neural networks must include an uncertainty estimation mechanism. Here we examine the relationship between deep architectures and their respective training regimes, with their corresponding selective prediction and uncertainty estimation performance. We consider some of the most popular estimation performance metrics previously proposed including AUROC, ECE, AURC as well as coverage for selective accuracy constraint. We present a novel and comprehensive study of selective prediction and the uncertainty estimation performance of 523 existing pretrain…
Paris-Saclay University（巴黎萨克雷大学）；ENSTA Paris（巴黎高等先进技术学院）；Institut Polytechnique de Paris（巴黎理工学院）
Monocular depth is important in many tasks, such as 3D reconstruction and autonomous driving. Deep learning based models achieve state-of-the-art performance in this field. A set of novel approaches for estimating monocular depth consists of transforming the regression task into a classification one. However, there is a lack of detailed descriptions and comparisons for Classification Approaches for Regression (CAR) in the community and no in-depth exploration of their potential for uncertainty estimation. To this end, this paper will introduce a taxonomy and summary of CAR approaches, a new un…
Uncertainty estimation in deep learning has become a leading research field in medical image analysis due to the need for safe utilisation of AI algorithms in clinical practice. Most approaches for uncertainty estimation require sampling the network weights multiple times during testing or training multiple networks. This leads to higher training and testing costs in terms of time and computational resources. In this paper, we propose Layer Ensembles, a novel uncertainty estimation method that uses a single network and requires only a single pass to estimate predictive uncertainty of a network…
Numerous recent works utilize bi-Lipschitz regularization of neural network layers to preserve relative distances between data instances in the feature spaces of each layer. This distance sensitivity with respect to the data aids in tasks such as uncertainty calibration and out-of-distribution (OOD) detection. In previous works, features extracted with a distance sensitive model are used to construct feature covariance matrices which are used in deterministic uncertainty estimation or OOD detection. However, in cases where there is a distribution over tasks, these methods result in covariances…
Bayesian neural networks (BNN) and deep ensembles are principled approaches to estimate the predictive uncertainty of a deep learning model. However their practicality in real-time, industrial-scale applications are limited due to their heavy memory and inference cost. This motivates us to study principled approaches to high-quality uncertainty estimation that require only a single deep neural network (DNN). By formalizing the uncertainty quantification as a minimax learning problem, we first identify input distance awareness, i.e., the model's ability to quantify the distance of a testing exa…
Accurate and Reliable Uncertainty Estimates for Deterministic Predictions Extensions to Under and Overpredictions
Sandia National Laboratories（桑迪亚国家实验室）；Queen Mary University of London（伦敦玛丽女王大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）；National Center for Atmospheric Research（美国国家大气研究中心）
University of Notre Dame（圣母大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Accurately estimating uncertainties in neural network predictions is of great importance in building trusted DNNs-based models, and there is an increasing interest in providing accurate uncertainty estimation on many tasks, such as security cameras and autonomous driving vehicles. In this paper, we focus on the two main use cases of uncertainty estimation, i.e. selective prediction and confidence calibration. We first reveal potential issues of commonly used quality metrics for uncertainty estimation in both use cases, and propose our new metrics to mitigate them. We then apply these new metri…
We extend Deep Deterministic Uncertainty (DDU), a method for uncertainty estimation using feature space densities, to semantic segmentation. DDU enables quantifying and disentangling epistemic and aleatoric uncertainty in a single forward pass through the model. We study the similarity of feature representations of pixels at different locations for the same class and conclude that it is feasible to apply DDU location independently, which leads to a significant reduction in memory consumption compared to pixel dependent DDU. Using the DeepLab-v3+ architecture on Pascal VOC 2012, we show that DD…
When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for example, uncertainty that is intrinsic to the training set may be well-handled by a Bayesian approach, while uncertainty introduced by shifts between training and query distributions may be better-addressed by density/support estimation. In this paper, we examine three types of uncertainty: model capacity uncertainty, intrinsic data uncertainty, and open set unce…
National Research University Higher School of Economics（国家研究型高等经济大学）；Samsung AI Center Moscow（三星莫斯科人工智能中心）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）
Uncertainty estimation and ensembling methods go hand-in-hand. Uncertainty estimation is one of the main benchmarks for assessment of ensembling performance. At the same time, deep learning ensembles have provided state-of-the-art results in uncertainty estimation. In this work, we focus on in-domain uncertainty for image classification. We explore the standards for its quantification and point out pitfalls of existing metrics. Avoiding these pitfalls, we perform a broad study of different ensembling techniques. To provide more insight in this study, we introduce the deep ensemble equivalent s…
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…
We propose a method to estimate the uncertainty of the outcome of an image classifier on a given input datum. Deep neural networks commonly used for image classification are deterministic maps from an input image to an output class. As such, their outcome on a given datum involves no uncertainty, so we must specify what variability we are referring to when defining, measuring and interpreting uncertainty, and attributing "confidence" to the outcome. To this end, we introduce the Wellington Posterior, which is the distribution of outcomes that would have been obtained in response to data that c…
Offline reinforcement learning, wherein one uses off-policy data logged by a fixed behavior policy to evaluate and learn new policies, is crucial in applications where experimentation is limited such as medicine. We study the estimation of policy value and gradient of a deterministic policy from off-policy data when actions are continuous. Targeting deterministic policies, for which action is a deterministic function of state, is crucial since optimal policies are always deterministic (up to ties). In this setting, standard importance sampling and doubly robust estimators for policy value and …
Virginia Tech（弗吉尼亚理工大学）；Virginia Tech Transportation Institute（弗吉尼亚理工交通研究所）
Past research on pedestrian trajectory forecasting mainly focused on deterministic predictions which provide only point estimates of future states. These future estimates can help an autonomous vehicle plan its trajectory and avoid collision. However, under dynamic traffic scenarios, planning based on deterministic predictions is not trustworthy. Rather, estimating the uncertainty associated with the predicted states with a certain level of confidence can lead to robust path planning. Hence, the authors propose to quantify this uncertainty during forecasting using stochastic approximation whic…
Deep neural networks (DNNs) have made a revolution in numerous fields during the last decade. However, in tasks with high safety requirements, such as medical or autonomous driving applications, providing an assessment of the models reliability can be vital. Uncertainty estimation for DNNs has been addressed using Bayesian methods, providing mathematically founded models for reliability assessment. These model are computationally expensive and generally impractical for many real-time use cases. Recently, non-Bayesian methods were proposed to tackle uncertainty estimation more efficiently. We p…
In a data-scarce field such as healthcare, where models often deliver predictions on patients with rare conditions, the ability to measure the uncertainty of a model's prediction could potentially lead to improved effectiveness of decision support tools and increased user trust. This work advances the understanding of uncertainty estimation for classification and risk prediction on medical tabular data, in a two-fold way. First, we expand and refine the set of heuristics to select an uncertainty estimation technique, introducing tests for clinically-relevant scenarios such as generalization to…
Yandex（扬德克斯）；Higher School of Economics（高等经济学院）；University of Cambridge（剑桥大学）
Uncertainty estimation is important for ensuring safety and robustness of AI systems. While most research in the area has focused on un-structured prediction tasks, limited work has investigated general uncertainty estimation approaches for structured prediction. Thus, this work aims to investigate uncertainty estimation for autoregressive structured prediction tasks within a single unified and interpretable probabilistic ensemble-based framework. We consider: uncertainty estimation for sequence data at the token-level and complete sequence-level; interpretations for, and applications of, vari…
