Many methods have been proposed to quantify the predictive uncertainty associated with the outputs of deep neural networks. Among them, ensemble methods often lead to state-of-the-art results, though they require modifications to the training procedures and are computationally costly for both training and inference. In this paper, we propose a new single-model based approach. The main idea is inspired by the observation that we can "simulate" an ensemble of models by drawing from a Gaussian distribution, with a form similar to those from the asymptotic normality theory, infinitesimal Jackknife, Laplacian approximation to Bayesian neural networks, and trajectories in stochastic gradient descents. However, instead of using each model in the "ensemble" to predict and then aggregating their predictions, we integrate the Gaussian distribution and the softmax outputs of the neural networks. We use a mean-field approximation formula to compute this analytically intractable integral. The proposed approach has several appealing properties: it functions as an ensemble without requiring multiple models, and it enables closed-form approximate inference using only the first and second moments of the Gaussian. Empirically, the proposed approach performs competitively when compared to state-of-the-art methods, including deep ensembles, temperature scaling, dropout and Bayesian NNs, on standard uncertainty estimation tasks. It also outperforms many methods on out-of-distribution detection.
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…
Tsinghua University（清华大学）；University of Cambridge（剑桥大学）
It is often remarked that neural networks fail to increase their uncertainty when predicting on data far from the training distribution. Yet naively using softmax confidence as a proxy for uncertainty achieves modest success in tasks exclusively testing for this, e.g., out-of-distribution (OOD) detection. This paper investigates this contradiction, identifying two implicit biases that do encourage softmax confidence to correlate with epistemic uncertainty: 1) Approximately optimal decision boundary structure, and 2) Filtering effects of deep networks. It describes why low-dimensional intuition…
University of Tübingen（图宾根大学）；Max-Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
In Bayesian Deep Learning, distributions over the output of classification neural networks are often approximated by first constructing a Gaussian distribution over the weights, then sampling from it to receive a distribution over the softmax outputs. This is costly. We reconsider old work (Laplace Bridge) to construct a Dirichlet approximation of this softmax output distribution, which yields an analytic map between Gaussian distributions in logit space and Dirichlet distributions (the conjugate prior to the Categorical distribution) in the output space. Importantly, the vanilla Laplace Bridg…
Neural networks utilize the softmax as a building block in classification tasks, which contains an overconfidence problem and lacks an uncertainty representation ability. As a Bayesian alternative to the softmax, we consider a random variable of a categorical probability over class labels. In this framework, the prior distribution explicitly models the presumed noise inherent in the observed label, which provides consistent gains in generalization performance in multiple challenging tasks. The proposed method inherits advantages of Bayesian approaches that achieve better uncertainty estimation…
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…
For a broad variety of critical applications, it is essential to know how confident a classification prediction is. In this paper, we discuss the drawbacks of softmax to calculate class probabilities and to handle uncertainty in Bayesian neural networks. We introduce a new kind of prediction layer called radial prediction layer (RPL) to overcome these issues. In contrast to the softmax classification, RPL is based on the open-world assumption. Therefore, the class prediction probabilities are much more meaningful to assess the uncertainty concerning the novelty of the input. We show that neura…
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…
National University of Singapore（新加坡国立大学）；Untangle AI（Untangle人工智能公司）
Existing uncertainty modeling approaches try to detect an out-of-distribution point from the in-distribution dataset. We extend this argument to detect finer-grained uncertainty that distinguishes between (a). certain points, (b). uncertain points but within the data distribution, and (c). out-of-distribution points. Our method corrects overconfident NN decisions, detects outlier points and learns to say ``I don't know'' when uncertain about a critical point between the top two predictions. In addition, we provide a mechanism to quantify class distributions overlap in the decision manifold and…
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…
Neural Network (NN) classifiers can assign extreme probabilities to samples that have not appeared during training (out-of-distribution samples) resulting in erroneous and unreliable predictions. One of the causes for this unwanted behaviour lies in the use of the standard softmax operator which pushes the posterior probabilities to be either zero or unity hence failing to model uncertainty. The statistical derivation of the softmax operator relies on the assumption that the distributions of the latent variables for a given class are Gaussian with known variance. However, it is possible to use…
Uncertainty-Aware Calibrated Clinical Text Classification with Large Language Models
Faculty of Dental Medicine and Oral Health Sciences, McGill University（牙医学院与口腔健康科学学院，麦吉尔大学）；McGill University（麦吉尔大学）；Mila–Quebec Artificial Intelligence Institute（魁北克人工智能研究所）；School of Computer Science, McGill University（计算机科学学院，麦吉尔大学）
Universidade Federal de Pernambuco（伯南布哥联邦大学）；Montreal Institute for Learning Algorithms, University of Montreal（蒙特利尔大学蒙特利尔学习算法研究所）
Building robust deterministic neural networks remains a challenge. On the one hand, some approaches improve out-of-distribution detection at the cost of reducing classification accuracy in some situations. On the other hand, some methods simultaneously increase classification accuracy, uncertainty estimation, and out-of-distribution detection at the expense of reducing the inference efficiency. In this paper, we propose training deterministic neural networks using our DisMax loss, which works as a drop-in replacement for the usual SoftMax loss (i.e., the combination of the linear output layer,…
Tianjin University（天津大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Uncertainty estimation is critical for cost-sensitive deep-learning applications (i.e. disease diagnosis). It is very challenging partly due to the inaccessibility of uncertainty groundtruth in most datasets. Previous works proposed to estimate the uncertainty from softmax calibration, Monte Carlo sampling, subjective logic and so on. However, these existing methods tend to be over-confident about their predictions with unreasonably low overall uncertainty, which originates from the imbalance between positive (correct classifications) and negative (incorrect classifications) samples. For this …
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认知智能与计算实验室）；Department of Computer Science, The University of Manchester, United Kingdom（英国曼彻斯特大学计算机科学系）；Manchester Centre for AI Fundamentals, Manchester, United Kingdom（英国曼彻斯特人工智能基础研究中心）；Rational Intelligence Lab, CISPA Helmholtz Center for Information Security, Germany（德国CISPA海德堡信息安全中心理性智能实验室）
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 …
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Washington（华盛顿大学）
Mixup~\cite{zhang2017mixup} is a recently proposed method for training deep neural networks where additional samples are generated during training by convexly combining random pairs of images and their associated labels. While simple to implement, it has been shown to be a surprisingly effective method of data augmentation for image classification: DNNs trained with mixup show noticeable gains in classification performance on a number of image classification benchmarks. In this work, we discuss a hitherto untouched aspect of mixup training -- the calibration and predictive uncertainty of model…
Technische Universität Dortmund（多特蒙德工业大学）；Bergische Universität Wuppertal（伍珀塔尔大学）
We study the quantification of uncertainty of Convolutional Neural Networks (CNNs) based on gradient metrics. Unlike the classical softmax entropy, such metrics gather information from all layers of the CNN. We show for the EMNIST digits data set that for several such metrics we achieve the same meta classification accuracy -- i.e. the task of classifying predictions as correct or incorrect without knowing the actual label -- as for entropy thresholding. We apply meta classification to unknown concepts (out-of-distribution samples) -- EMNIST/Omniglot letters, CIFAR10 and noise -- and demonstra…
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…
Label Smoothing (LS) improves model generalization through penalizing models from generating overconfident output distributions. For each training sample the LS strategy smooths the one-hot encoded training signal by distributing its distribution mass over the non-ground truth classes. We extend this technique by considering example pairs, coined PLS. PLS first creates midpoint samples by averaging random sample pairs and then learns a smoothing distribution during training for each of these midpoint samples, resulting in midpoints with high uncertainty labels for training. We empirically show…
A crucial requirement for reliable deployment of deep learning models for safety-critical applications is the ability to identify out-of-distribution (OOD) data points, samples which differ from the training data and on which a model might underperform. Previous work has attempted to tackle this problem using uncertainty estimation techniques. However, there is empirical evidence that a large family of these techniques do not detect OOD reliably in classification tasks. This paper gives a theoretical explanation for said experimental findings and illustrates it on synthetic data. We prove that…
Uncertainty-Aware Out-of-Distribution Detection with Gaussian Processes
Michigan State University（密歇根州立大学）；School of Computer Science（计算机科学学院）；University of Michigan Transportation Research Institute（密歇根大学交通研究所）；Carnegie Mellon University（卡内基梅隆大学）；University of Michigan（密歇根大学）
Modern deep learning models have achieved great success in predictive accuracy for many data modalities. However, their application to many real-world tasks is restricted by poor uncertainty estimates, such as overconfidence on out-of-distribution (OOD) data and ungraceful failing under distributional shift. Previous benchmarks have found that ensembles of neural networks (NNs) are typically the best calibrated models on OOD data. Inspired by this, we leverage recent theoretical advances that characterize the function-space prior of an ensemble of infinitely-wide NNs as a Gaussian process, ter…
Emergence of artificial intelligence techniques in biomedical applications urges the researchers to pay more attention on the uncertainty quantification (UQ) in machine-assisted medical decision making. For classification tasks, prior studies on UQ are difficult to compare with each other, due to the lack of a unified quantitative evaluation metric. Considering that well-performing UQ models ought to know when the classification models act incorrectly, we design a new evaluation metric, area under Confidence-Classification Characteristic curves (AUCCC), to quantitatively evaluate the performan…
Deep neural networks present impressive performance, yet they cannot reliably estimate their predictive confidence, limiting their applicability in high-risk domains. We show that applying a multi-label one-vs-all loss reveals classification ambiguity and reduces model overconfidence. The introduced SLOVA (Single Label One-Vs-All) model redefines typical one-vs-all predictive probabilities to a single label situation, where only one class is the correct answer. The proposed classifier is confident only if a single class has a high probability and other probabilities are negligible. Unlike the …
On Impact of Loss Function on the Performance of Neural Networks in Melanoma Diagnosis
Technological University Dublin（都柏林理工大学）；Research Ireland Centre for Research Training in Machine Learning, ML-Labs（爱尔兰研究中心机器学习研究培训中心，机器学习实验室）；Dublin City University（都柏林城市大学）；University College Dublin（都柏林大学学院）
Test Input Prioritizers (TIP) for Deep Neural Networks (DNN) are an important technique to handle the typically very large test datasets efficiently, saving computation and labeling costs. This is particularly true for large-scale, deployed systems, where inputs observed in production are recorded to serve as potential test or training data for the next versions of the system. Feng et. al. propose DeepGini, a very fast and simple TIP, and show that it outperforms more elaborate techniques such as neuron- and surprise coverage. In a large-scale study (4 case studies, 8 test datasets, 32'200 tra…
Institute of Mathematics, EPFL, Switzerland（瑞士联邦理工学院数学研究所）；Computational Engineering Lab, Empa, Switzerland（瑞士Empa计算工程实验室）；ENSAE, IP Paris, France（法国IP巴黎高等商学院）
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Out-of-distribution (OOD) detection is critical for preventing deep learning models from making incorrect predictions to ensure the safety of artificial intelligence systems. Especially in safety-critical applications such as medical diagnosis and autonomous driving, the cost of incorrect decisions is usually unbearable. However, neural networks often suffer from the overconfidence issue, making high confidence for OOD data which are never seen during training process and may be irrelevant to training data, namely in-distribution (ID) data. Determining the reliability of the prediction is stil…
Microsoft Research Asia（微软亚洲研究院）；MILA（米拉研究所）；S-Lab, Nanyang Technological University（南洋理工大学S-Lab实验室）；Nanyang Technological University（南洋理工大学）
Confidence calibration is of great importance to the reliability of decisions made by machine learning systems. However, discriminative classifiers based on deep neural networks are often criticized for producing overconfident predictions that fail to reflect the true correctness likelihood of classification accuracy. We argue that such an inability to model uncertainty is mainly caused by the closed-world nature in softmax: a model trained by the cross-entropy loss will be forced to classify input into one of $K$ pre-defined categories with high probability. To address this problem, we for th…
ISCTE – Instituto Universitário de Lisboa（里斯本大学学院）；PDMFC；IT – Instituto de Telecomunicações（电信研究所）；FCT – Universidade Nova de Lisboa（新里斯本大学科学与技术学院）；CTTC - Centre Tecnològic de Telecomunicacions de Catalunya（加泰罗尼亚电信技术中心）
Only increasing accuracy without considering uncertainty may negatively impact Deep Neural Network (DNN) decision-making and decrease its reliability. This paper proposes five combined preprocessing and post-processing methods for time-series binary classification problems that simultaneously increase the accuracy and reliability of DNN outputs applied in a 5G UAV security dataset. These techniques use DNN outputs as input parameters and process them in different ways. Two methods use a well-known Machine Learning (ML) algorithm as a complement, and the other three use only confidence values t…
The softmax function is a ubiquitous component at the output of neural networks and increasingly in intermediate layers as well. This paper provides convex lower bounds and concave upper bounds on the softmax function, which are compatible with convex optimization formulations for characterizing neural networks and other ML models. We derive bounds using both a natural exponential-reciprocal decomposition of the softmax as well as an alternative decomposition in terms of the log-sum-exp function. The new bounds are provably and/or numerically tighter than linear bounds obtained in previous wor…
Out-of-Distribution (OoD) inputs are examples that do not belong to the true underlying distribution of the dataset. Research has shown that deep neural nets make confident mispredictions on OoD inputs. Therefore, it is critical to identify OoD inputs for safe and reliable deployment of deep neural nets. Often a threshold is applied on a similarity score to detect OoD inputs. One such similarity is angular similarity which is the dot product of latent representation with the mean class representation. Angular similarity encodes uncertainty, for example, if the angular similarity is less, it is…
In the semantic segmentation of street scenes the reliability of the prediction and therefore uncertainty measures are of highest interest. We present a method that generates for each input image a hierarchy of nested crops around the image center and presents these, all re-scaled to the same size, to a neural network for semantic segmentation. The resulting softmax outputs are then post processed such that we can investigate mean and variance over all image crops as well as mean and variance of uncertainty heat maps obtained from pixel-wise uncertainty measures, like the entropy, applied to e…
