In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to ensure alignment between predicted probabilities and actual outcomes. However, when score heterogeneity deviates from the underlying data probability distribution, traditional calibration metrics lose reliability, failing to align score distribution with actual probabilities. In this study, we highlight approaches that prioritize optimizing the alignment between predicted scores and true probability distributions over minimizing traditional performance or calibration metrics. When employing tree-based models such as Random Forest and XGBoost, our analysis emphasizes the flexibility these models offer in tuning hyperparameters to minimize the Kullback-Leibler (KL) divergence between predicted and true distributions. Through extensive empirical analysis across 10 UCI datasets and simulations, we demonstrate that optimizing tree-based models based on KL divergence yields superior alignment between predicted scores and actual probabilities without significant performance loss. In real-world scenarios, the reference probability is determined a priori as a Beta distribution estimated through maximum likelihood. Conversely, minimizing traditional calibration metrics may lead to suboptimal results, characterized by notable performance declines and inferior KL values. Our findings reveal limitations in traditional calibration metrics, which could undermine the reliability of predictive models for critical decision-making.
University of Oulu（奥卢大学）；Oura Health Ltd.（欧拉健康有限公司）
Classifier calibration does not always go hand in hand with the classifier's ability to separate the classes. There are applications where good classifier calibration, i.e. the ability to produce accurate probability estimates, is more important than class separation. When the amount of data for training is limited, the traditional approach to improve calibration starts to crumble. In this article we show how generating more data for calibration is able to improve calibration algorithm performance in many cases where a classifier is not naturally producing well-calibrated outputs and the tradi…
Binary classification is highly used in credit scoring in the estimation of probability of default. The validation of such predictive models is based both on rank ability, and also on calibration (i.e. how accurately the probabilities output by the model map to the observed probabilities). In this study we cover the current best practices regarding calibration for binary classification, and explore how different approaches yield different results on real world credit scoring data. The limitations of evaluating credit scoring models using only rank ability metrics are explored. A benchmark is r…
Deep learning has achieved many breakthroughs in modern classification tasks. Numerous architectures have been proposed for different data structures but when it comes to the loss function, the cross-entropy loss is the predominant choice. Recently, several alternative losses have seen revived interests for deep classifiers. In particular, empirical evidence seems to promote square loss but a theoretical justification is still lacking. In this work, we contribute to the theoretical understanding of square loss in classification by systematically investigating how it performs for overparametriz…
Single-trial classification of event-related potentials in electroencephalogram (EEG) signals is a very important paradigm of brain-computer interface (BCI). Because of individual differences, usually some subject-specific calibration data are required to tailor the classifier for each subject. Transfer learning has been extensively used to reduce such calibration data requirement, by making use of auxiliary data from similar/relevant subjects/tasks. However, all previous research assumes that all auxiliary data have been labeled. This paper considers a more general scenario, in which part of …
Adaptive Semi-Supervised Training of P300 ERP-BCI Speller System with Minimum Calibration Effort
Department of Biostatistics and Bioinformatics（生物统计学与生物信息学系）；Rollins School of Public Health, Emory University（埃默里大学罗林斯公共卫生学院）；Department of Physical Medicine and Rehabilitation（物理医学与康复系）；Department of Biomedical Engineering（生物医学工程系）；University of Michigan（密歇根大学）
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…
Learning accurate probabilistic models from data is crucial in many practical tasks in data mining. In this paper we present a new non-parametric calibration method called \textit{ensemble of near isotonic regression} (ENIR). The method can be considered as an extension of BBQ, a recently proposed calibration method, as well as the commonly used calibration method based on isotonic regression. ENIR is designed to address the key limitation of isotonic regression which is the monotonicity assumption of the predictions. Similar to BBQ, the method post-processes the output of a binary classifier …
University of Piuttsburgh（匹兹堡大学）；University of Pittsburgh（匹兹堡大学）
Accurate calibration of probabilistic predictive models learned is critical for many practical prediction and decision-making tasks. There are two main categories of methods for building calibrated classifiers. One approach is to develop methods for learning probabilistic models that are well-calibrated, ab initio. The other approach is to use some post-processing methods for transforming the output of a classifier to be well calibrated, as for example histogram binning, Platt scaling, and isotonic regression. One advantage of the post-processing approach is that it can be applied to any exist…
Objective: Using traditional approaches, a Brain-Computer Interface (BCI) requires the collection of calibration data for new subjects prior to online use. Calibration time can be reduced or eliminated e.g.~by transfer of a pre-trained classifier or unsupervised adaptive classification methods which learn from scratch and adapt over time. While such heuristics work well in practice, none of them can provide theoretical guarantees. Our objective is to modify an event-related potential (ERP) paradigm to work in unison with the machine learning decoder to achieve a reliable calibration-less decod…
To increase the trustworthiness of deep neural network (DNN) classifiers, an accurate prediction confidence that represents the true likelihood of correctness is crucial. Towards this end, many post-hoc calibration methods have been proposed to leverage a lightweight model to map the target DNN's output layer into a calibrated confidence. Nonetheless, on an out-of-distribution (OOD) dataset in practice, the target DNN can often mis-classify samples with a high confidence, creating significant challenges for the existing calibration methods to produce an accurate confidence. In this paper, we p…
In many applications, it is desirable that a classifier not only makes accurate predictions, but also outputs calibrated posterior probabilities. However, many existing classifiers, especially deep neural network classifiers, tend to be uncalibrated. Post-hoc calibration is a technique to recalibrate a model by learning a calibration map. Existing approaches mostly focus on constructing calibration maps with low calibration errors, however, this quality is inadequate for a calibrator being useful. In this paper, we introduce two constraints that are worth consideration in designing a calibrati…
University of Maryland, College Park（马里兰大学帕克分校）；Software Engineering Institute（软件工程研究所）；Carnegie Mellon University（卡内基梅隆大学）
Classifier calibration has received recent attention from the machine learning community due both to its practical utility in facilitating decision making, as well as the observation that modern neural network classifiers are poorly calibrated. Much of this focus has been towards the goal of learning classifiers such that their output with largest magnitude (the "predicted class") is calibrated. However, this narrow interpretation of classifier outputs does not adequately capture the variety of practical use cases in which classifiers can aid in decision making. In this work, we argue that mor…
University of Piuttsburgh（匹兹堡大学）；University of Pittsburgh（匹兹堡大学）
A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning models are used in decision analysis. This paper presents two new non-parametric methods for calibrating outputs of binary classification models: a method based on the Bayes optimal selection and a method based on the Bayesian model averaging. The advantage of these methods is that they are independent of the algorithm used to learn a predictive model, and th…
appliedAI Institute gGmbH（应用人工智能研究所（非营利有限责任公司））；appliedAI Initiative GmbH（应用人工智能倡议有限公司）
For many applications of probabilistic classifiers it is important that the predicted confidence vectors reflect true probabilities (one says that the classifier is calibrated). It has been shown that common models fail to satisfy this property, making reliable methods for measuring and improving calibration important tools. Unfortunately, obtaining these is far from trivial for problems with many classes. We propose two techniques that can be used in tandem. First, a reduced calibration method transforms the original problem into a simpler one. We prove for several notions of calibration that…
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…
Uppsala University（乌普萨拉大学）；Veoneer Inc.（维宁尔公司）；Linköping University（林雪平大学）
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their ability to represent uncertainty about predictions. In safety-critical applications, it is pivotal for a model to possess an adequate sense of uncertainty, which for probabilistic classifiers translates into outputting probability distributions that are consistent with the empirical frequencies observed from realized outcomes. A classifier with such a propert…
University of Victoria（维多利亚大学）；Helwan University（赫勒万大学）
This paper explores the calibration of a classifier output score in binary classification problems. A calibrator is a function that maps the arbitrary classifier score, of a testing observation, onto $[0,1]$ to provide an estimate for the posterior probability of belonging to one of the two classes. Calibration is important for two reasons; first, it provides a meaningful score, that is the posterior probability; second, it puts the scores of different classifiers on the same scale for comparable interpretation. The paper presents three main contributions: (1) Introducing multi-score calibrati…
Uncertainty Calibration of Multi-Label Bird Sound Classifiers
INS, Kiel University, Germany（基尔大学）；Tilburg University, Netherlands（蒂尔堡大学）；Naturalis Biodiversity Center, Netherlands（自然史生物多样性中心）；IES, University of Kassel, Germany（卡塞尔大学）
We address two major obstacles to practical use of supervised classifiers on distributed private data. Whether a classifier was trained by a federation of cooperating clients or trained centrally out of distribution, (1) the output scores must be calibrated, and (2) performance metrics must be evaluated -- all without assembling labels in one place. In particular, we show how to perform calibration and compute precision, recall, accuracy and ROC-AUC in the federated setting under three privacy models (i) secure aggregation, (ii) distributed differential privacy, (iii) local differential privac…
Deep Neural Network Calibration by Reducing Classifier Shift with Stochastic Masking
School of Artificial Intelligence, Jilin University（吉林大学人工智能学院）；CSIRO's Data61 and Monash University (adjunct)（CSIRO的数据61与墨尔本大学（兼职））；King Abdullah University of Science and Technology（国王阿卜杜勒阿齐兹科技大学）
Balancing Two Classifiers via A Simplex ETF Structure for Model Calibration
School of Artificial Intelligence, Jilin University（吉林大学人工智能学院）；CSIRO’s Data61（联邦科学与工业研究组织Data61研究院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
University of California, Berkeley（加州大学伯克利分校）；University of Chicago（芝加哥大学）
Intermediate-Severity (IS) faults present milder symptoms compared to severe faults, and are more difficult to detect and diagnose due to their close resemblance to normal operating conditions. The lack of IS fault examples in the training data can pose severe risks to Fault Detection and Diagnosis (FDD) methods that are built upon Machine Learning (ML) techniques, because these faults can be easily mistaken as normal operating conditions. Ensemble models are widely applied in ML and are considered promising methods for detecting out-of-distribution (OOD) data. We identify common pitfalls in t…
Trustworthy classifiers are essential to the adoption of machine learning predictions in many real-world settings. The predicted probability of possible outcomes can inform high-stakes decision making, particularly when assessing the expected value of alternative decisions or the risk of bad outcomes. These decisions require well-calibrated probabilities, not just the correct prediction of the most likely class. Black-box classifier calibration methods can improve the reliability of a classifier's output without requiring retraining. However, these methods are unable to detect subpopulations w…
University of Tuebingen（蒂宾根大学）；TU Munich（慕尼黑工业大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；German Aerospace Center (DLR)（德国航空航天中心）
Many applications of classification methods not only require high accuracy but also reliable estimation of predictive uncertainty. However, while many current classification frameworks, in particular deep neural networks, achieve high accuracy, they tend to incorrectly estimate uncertainty. In this paper, we propose a method that adjusts the confidence estimates of a general classifier such that they approach the probability of classifying correctly. In contrast to existing approaches, our calibration method employs a non-parametric representation using a latent Gaussian process, and is specif…
Ping An Technology (Shenzhen) Co., Ltd.（平安科技（深圳）有限公司）；University of Science and Technology of China（中国科学技术大学）
Although deep Neural Networks (DNNs) have achieved tremendous success in audio classification tasks, their uncertainty calibration are still under-explored. A well-calibrated model should be accurate when it is certain about its prediction and indicate high uncertainty when it is likely to be inaccurate. In this work, we investigate the uncertainty calibration for deep audio classifiers. In particular, we empirically study the performance of popular calibration methods: (i) Monte Carlo Dropout, (ii) ensemble, (iii) focal loss, and (iv) spectral-normalized Gaussian process (SNGP), on audio clas…
The University of Tokyo（东京大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所高级智能项目中心）
We investigate the problem of multiclass classification with rejection, where a classifier can choose not to make a prediction to avoid critical misclassification. First, we consider an approach based on simultaneous training of a classifier and a rejector, which achieves the state-of-the-art performance in the binary case. We analyze this approach for the multiclass case and derive a general condition for calibration to the Bayes-optimal solution, which suggests that calibration is hard to achieve by general loss functions unlike the binary case. Next, we consider another traditional approach…
PRECISE Center（PRECISE中心）；University of Pennsylvania（宾夕法尼亚大学）
Providing reliable model uncertainty estimates is imperative to enabling robust decision making by autonomous agents and humans alike. While recently there have been significant advances in confidence calibration for trained models, examples with poor calibration persist in most calibrated models. Consequently, multiple techniques have been proposed that leverage label-invariant transformations of the input (i.e., an input manifold) to improve worst-case confidence calibration. However, manifold-based confidence calibration techniques generally do not scale and/or require expensive retraining …
Lawrence Livermore National Laboratories（劳伦斯利弗莫尔国家实验室）
This paper studies the problem of post-hoc calibration of machine learning classifiers. We introduce the following desiderata for uncertainty calibration: (a) accuracy-preserving, (b) data-efficient, and (c) high expressive power. We show that none of the existing methods satisfy all three requirements, and demonstrate how Mix-n-Match calibration strategies (i.e., ensemble and composition) can help achieve remarkably better data-efficiency and expressive power while provably maintaining the classification accuracy of the original classifier. Mix-n-Match strategies are generic in the sense that…
A central challenge in training classification models in the real-world federated system is learning with non-IID data. To cope with this, most of the existing works involve enforcing regularization in local optimization or improving the model aggregation scheme at the server. Other works also share public datasets or synthesized samples to supplement the training of under-represented classes or introduce a certain level of personalization. Though effective, they lack a deep understanding of how the data heterogeneity affects each layer of a deep classification model. In this paper, we bridge …
Wroclaw University of Science and Technology（弗罗茨瓦夫科技大学）
A vital aspect of the classification based model construction process is the calibration of the scoring function. One of the weaknesses of the calibration process is that it does not take into account the information about the relative positions of the recognized objects in the feature space. To alleviate this limitation, in this paper, we propose a novel concept of calculating a scoring function based on the distance of the object from the decision boundary and its distance to the class centroid. An important property is that the proposed score function has the same nature for all linear base…
Post-Training Quantization of Generative and Discriminative LSTM Text Classifiers: A Study of Calibration, Class Balance, and Robustness
School of Mathematical and Data Sciences（数学与数据科学学院）；West Virginia University（西弗吉尼亚大学）；Department of Industrial and Management Systems Engineering（工业与管理系统工程系）
Google Brain（谷歌大脑）；Google Research（谷歌研究院）；Google Inc.（谷歌公司）
Overconfidence and underconfidence in machine learning classifiers is measured by calibration: the degree to which the probabilities predicted for each class match the accuracy of the classifier on that prediction. How one measures calibration remains a challenge: expected calibration error, the most popular metric, has numerous flaws which we outline, and there is no clear empirical understanding of how its choices affect conclusions in practice, and what recommendations there are to counteract its flaws. In this paper, we perform a comprehensive empirical study of choices in calibration meas…
National Taiwan University（台湾大学）；Carnegie Mellon University（卡内基梅隆大学）
Generative Adversarial Networks (GANs) is a powerful family of models that learn an underlying distribution to generate synthetic data. Many existing studies of GANs focus on improving the realness of the generated image data for visual applications, and few of them concern about improving the quality of the generated data for training other classifiers -- a task known as the model compatibility problem. As a consequence, existing GANs often prefer generating `easier' synthetic data that are far from the boundaries of the classifiers, and refrain from generating near-boundary data, which are k…
Rethinking Calibration for Early-Exit Neural Networks
Jagiellonian University（雅盖隆大学）；Warsaw University of Technology（华沙理工大学）；IDEAS Research Institute（IDEAS研究院）；Johns Hopkins University（约翰霍普金斯大学）；Doctoral School of Exact and Natural Sciences（精确与自然科学博士学院）
When probabilistic classifiers are trained and calibrated, the so-called grouping loss component of the calibration loss can easily be overlooked. Grouping loss refers to the gap between observable information and information actually exploited in the calibration exercise. We investigate the relation between grouping loss and the concept of sufficiency, identifying comonotonicity as a useful criterion for sufficiency. We revisit the probing reduction approach of Langford & Zadrozny (2005) and find that it produces an estimator of probabilistic classifiers that reduces grouping loss. Finally, w…
