We propose an algorithm combining calibrated prediction and generalization bounds from learning theory to construct confidence sets for deep neural networks with PAC guarantees---i.e., the confidence set for a given input contains the true label with high probability. We demonstrate how our approach can be used to construct PAC confidence sets on ResNet for ImageNet, a visual object tracking model, and a dynamics model for the half-cheetah reinforcement learning problem.
We consider using an ensemble of binary classifiers for transductive prediction, when unlabeled test data are known in advance. We derive minimax optimal rules for confidence-rated prediction in this setting. By using PAC-Bayes analysis on these rules, we obtain data-dependent performance guarantees without distributional assumptions on the data. Our analysis techniques are readily extended to a setting in which the predictor is allowed to abstain.
In this paper, we propose a confidence-calibration method for predicting the winner of a famous multiplayer online battle arena (MOBA) game, League of Legends. In MOBA games, the dataset may contain a large amount of input-dependent noise; not all of such noise is observable. Hence, it is desirable to attempt a confidence-calibrated prediction. Unfortunately, most existing confidence calibration methods are pertaining to image and document classification tasks where consideration on uncertainty is not crucial. In this paper, we propose a novel calibration method that takes data uncertainty int…
Deep metric learning has gained promising improvement in recent years following the success of deep learning. It has been successfully applied to problems in few-shot learning, image retrieval, and open-set classifications. However, measuring the confidence of a deep metric learning model and identifying unreliable predictions is still an open challenge. This paper focuses on defining a calibrated and interpretable confidence metric that closely reflects its classification accuracy. While performing similarity comparison directly in the latent space using the learned distance metric, our appro…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；University of Tübingen（图宾根大学）
Adversarial training yields robust models against a specific threat model, e.g., $L_\infty$ adversarial examples. Typically robustness does not generalize to previously unseen threat models, e.g., other $L_p$ norms, or larger perturbations. Our confidence-calibrated adversarial training (CCAT) tackles this problem by biasing the model towards low confidence predictions on adversarial examples. By allowing to reject examples with low confidence, robustness generalizes beyond the threat model employed during training. CCAT, trained only on $L_\infty$ adversarial examples, increases robustness ag…
Korea Advanced Institute of Science and Technology（韩国科学技术院）；University of Michigan（密歇根大学）；Google Brain（谷歌大脑）
The problem of detecting whether a test sample is from in-distribution (i.e., training distribution by a classifier) or out-of-distribution sufficiently different from it arises in many real-world machine learning applications. However, the state-of-art deep neural networks are known to be highly overconfident in their predictions, i.e., do not distinguish in- and out-of-distributions. Recently, to handle this issue, several threshold-based detectors have been proposed given pre-trained neural classifiers. However, the performance of prior works highly depends on how to train the classifiers s…
Université de Technologie de Compiègne（贡比涅技术大学）；Shanghai University（上海大学）
Evidential clustering is an approach to clustering in which cluster-membership uncertainty is represented by a collection of Dempster-Shafer mass functions forming an evidential partition. In this paper, we propose to construct these mass functions by bootstrapping finite mixture models. In the first step, we compute bootstrap percentile confidence intervals for all pairwise probabilities (the probabilities for any two objects to belong to the same class). We then construct an evidential partition such that the pairwise belief and plausibility degrees approximate the bounds of the confidence i…
PRECISE Center（PRECISE中心）；University of Pennsylvania（宾夕法尼亚大学）
A key challenge for deploying deep neural networks (DNNs) in safety critical settings is the need to provide rigorous ways to quantify their uncertainty. In this paper, we propose a novel algorithm for constructing predicted classification confidences for DNNs that comes with provable correctness guarantees. Our approach uses Clopper-Pearson confidence intervals for the Binomial distribution in conjunction with the histogram binning approach to calibrated prediction. In addition, we demonstrate how our predicted confidences can be used to enable downstream guarantees in two settings: (i) fast …
KAIST（韩国科学技术院）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；Kakao Enterprise；Inha University（仁荷大学）
Randomized smoothing is currently a state-of-the-art method to construct a certifiably robust classifier from neural networks against $\ell_2$-adversarial perturbations. Under the paradigm, the robustness of a classifier is aligned with the prediction confidence, i.e., the higher confidence from a smoothed classifier implies the better robustness. This motivates us to rethink the fundamental trade-off between accuracy and robustness in terms of calibrating confidences of a smoothed classifier. In this paper, we propose a simple training scheme, coined SmoothMix, to control the robustness of sm…
Deep neural networks (DNN) are prone to miscalibrated predictions, often exhibiting a mismatch between the predicted output and the associated confidence scores. Contemporary model calibration techniques mitigate the problem of overconfident predictions by pushing down the confidence of the winning class while increasing the confidence of the remaining classes across all test samples. However, from a deployment perspective, an ideal model is desired to (i) generate well-calibrated predictions for high-confidence samples with predicted probability say >0.95, and (ii) generate a higher proportio…
University of Tartu（塔尔图大学）；University of Bristol（布里斯托尔大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；The Alan Turing Institute（艾伦·图灵研究所）
Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective multiplicative factor for inputs to the last softmax layer. On non-neural models the existing methods apply binary calibration in a pairwise or one-vs-rest fashion. We propose a natively multiclass calibration method applicable to classifiers from any model class, derived from Dirichlet distributions and generalising the beta calibration method from binary classificat…
Protein-protein interactions (PPIs) are critical to normal cellular function and are related to many disease pathways. However, only 4% of PPIs are annotated with PTMs in biological knowledge databases such as IntAct, mainly performed through manual curation, which is neither time nor cost-effective. We use the IntAct PPI database to create a distant supervised dataset annotated with interacting protein pairs, their corresponding PTM type, and associated abstracts from the PubMed database. We train an ensemble of BioBERT models - dubbed PPI-BioBERT-x10 to improve confidence calibration. We ext…
Princeton University（普林斯顿大学）；Massachusetts Institute of Technology（麻省理工学院）；Johns Hopkins University（约翰斯·霍普金斯大学）
We propose a calibrated multivariate regression method named CMR for fitting high dimensional multivariate regression models. Compared with existing methods, CMR calibrates regularization for each regression task with respect to its noise level so that it simultaneously attains improved finite-sample performance and tuning insensitiveness. Theoretically, we provide sufficient conditions under which CMR achieves the optimal rate of convergence in parameter estimation. Computationally, we propose an efficient smoothed proximal gradient algorithm with a worst-case numerical rate of convergence $\…
Confidence-calibrated covariate shift correction for few-shot classification in Vision-Language Models
School of Mathematics and Computer Science, Institute of Business Administration（商业管理学院数学与计算机科学学院）；Center for Research in Computer Vision, University of Central Florida（中佛罗里达大学计算机视觉研究中心）；National University of Computer and Emerging Sciences（国家计算机与新兴科学大学）
University of Augsburg（奥格斯堡大学）；Imperial College London（帝国理工学院）
Ongoing developments in neural network models are continually advancing the state of the art in terms of system accuracy. However, the predicted labels should not be regarded as the only core output; also important is a well-calibrated estimate of the prediction uncertainty. Such estimates and their calibration are critical in many practical applications. Despite their obvious aforementioned advantage in relation to accuracy, contemporary neural networks can, generally, be regarded as poorly calibrated and as such do not produce reliable output probability estimates. Further, while post-proces…
C$^2$GSPG: Confidence-calibrated Group Sequence Policy Gradient towards Self-aware Reasoning
Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高陵人工智能学院）；Tsinghua University（清华大学）；Beijing Key Laboratory of Research on Large Models（北京大模型研究关键实验室）；Engineering Research Center of Next-Generation Intelligent Search（下一代智能搜索工程研究中心）
Technical University of Denmark（丹麦技术大学）；Rigshospitalet, Copenhagen University Hospital（哥本哈根大学医院 Rigshospitalet）；University of Copenhagen（哥本哈根大学）
Data-driven methods based on machine learning have the potential to accelerate computational analysis of atomic structures. In this context, reliable uncertainty estimates are important for assessing confidence in predictions and enabling decision making. However, machine learning models can produce badly calibrated uncertainty estimates and it is therefore crucial to detect and handle uncertainty carefully. In this work we extend a message passing neural network designed specifically for predicting properties of molecules and materials with a calibrated probabilistic predictive distribution. …
Fraunhofer Center for Machine Learning（弗劳恩霍夫机器学习中心）；Fraunhofer Institute for Industrial Mathematics ITWM（弗劳恩霍夫工业数学研究所ITWM）
We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confidence level for each of their predictions. In essence, the training of our classifier proceeds in two steps. In a first step, the training data is represented in a latent space whose geometry is induced by a regular $(n-1)$-dimensional simplex, $n$ being the number of classes. We design this represe…
A multiclass classifier is said to be top-label calibrated if the reported probability for the predicted class -- the top-label -- is calibrated, conditioned on the top-label. This conditioning on the top-label is absent in the closely related and popular notion of confidence calibration, which we argue makes confidence calibration difficult to interpret for decision-making. We propose top-label calibration as a rectification of confidence calibration. Further, we outline a multiclass-to-binary (M2B) reduction framework that unifies confidence, top-label, and class-wise calibration, among othe…
We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own ans…
Poznan University of Technology（波兹南理工大学）；Polish Academy of Sciences（波兰科学院）；MNM Bioscience（MNM生物科学公司）
Machine learning applications, especially in the fields of me\-di\-cine and social sciences, are slowly being subjected to increasing scrutiny. Similarly to sample size planning performed in clinical and social studies, lawmakers and funding agencies may expect statistical uncertainty estimations in machine learning applications that impact society. In this paper, we present an easy-to-use python package and web application for estimating prediction confidence intervals. The package offers eight different procedures to determine and justify the sample size and confidence of predictions from ho…
Beijing University of Posts and Telecommunications（北京邮电大学）
Despite Graph Neural Networks (GNNs) have achieved remarkable accuracy, whether the results are trustworthy is still unexplored. Previous studies suggest that many modern neural networks are over-confident on the predictions, however, surprisingly, we discover that GNNs are primarily in the opposite direction, i.e., GNNs are under-confident. Therefore, the confidence calibration for GNNs is highly desired. In this paper, we propose a novel trustworthy GNN model by designing a topology-aware post-hoc calibration function. Specifically, we first verify that the confidence distribution in a graph…
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）
In classification applications, we often want probabilistic predictions to reflect confidence or uncertainty. Dropout, a commonly used training technique, has recently been linked to Bayesian inference, yielding an efficient way to quantify uncertainty in neural network models. However, as previously demonstrated, confidence estimates computed with a naive implementation of dropout can be poorly calibrated, particularly when using convolutional networks. In this paper, through the lens of ensemble learning, we associate calibration error with the correlation between the models sampled with dro…
Rutgers University（罗格斯大学）；Harvard University（哈佛大学）；National University of Singapore（新加坡国立大学）；Stanford University（斯坦福大学）
In many machine learning applications, it is important for the model to provide confidence scores that accurately capture its prediction uncertainty. Although modern learning methods have achieved great success in predictive accuracy, generating calibrated confidence scores remains a major challenge. Mixup, a popular yet simple data augmentation technique based on taking convex combinations of pairs of training examples, has been empirically found to significantly improve confidence calibration across diverse applications. However, when and how Mixup helps calibration is still a mystery. In th…
Distribution-Free Confidence Ellipsoids for Ridge Regression with PAC Bounds
Institute for Computer Science；Control (SZTAKI), Hungarian Research Network (HUN-REN), 13-17 Kende utca, H-1111, Budapest, Hungary (e-mail: ).；Department of Probability Theory；Statistics, Institute of Mathematics, E\"otv\"os Lor\'；University (ELTE), 1/C Pázmány Péter sétány, H-1117, Budapest, Hungary (e-mail: )
