Uncertainty in probabilistic classifiers predictions is a key concern when models are used to support human decision making, in broader probabilistic pipelines or when sensitive automatic decisions have to be taken. Studies have shown that most models are not intrinsically well calibrated, meaning that their decision scores are not consistent with posterior probabilities. Hence being able to calibrate these models, or enforce calibration while learning them, has regained interest in recent literature. In this context, properly assessing calibration is paramount to quantify new contributions tackling calibration. However, there is room for improvement for commonly used metrics and evaluation of calibration could benefit from deeper analyses. Thus this paper focuses on the empirical evaluation of calibration metrics in the context of classification. More specifically it evaluates different estimators of the Expected Calibration Error ($ECE$), amongst which legacy estimators and some novel ones, proposed in this paper. We build an empirical procedure to quantify the quality of these $ECE$ estimators, and use it to decide which estimator should be used in practice for different settings.
Evaluating Posterior Probabilities: Decision Theory, Proper Scoring Rules, and Calibration
Instituto de Ciencias de la Computación（计算机科学研究所）；Universidad de Buenos Aires - CONICET（布宜诺斯艾利斯大学 - 阿根廷国家科学与技术研究理事会）；Escuela Politécnica Superior, Universidad Autónoma de Madrid（马德里自治大学高等理工学院）
A well-calibrated neural model produces confidence (probability outputs) closely approximated by the expected accuracy. While prior studies have shown that mixup training as a data augmentation technique can improve model calibration on image classification tasks, little is known about using mixup for model calibration on natural language understanding (NLU) tasks. In this paper, we explore mixup for model calibration on several NLU tasks and propose a novel mixup strategy for pre-trained language models that improves model calibration further. Our proposed mixup is guided by both the Area Und…
Optimizing Estimators of Squared Calibration Errors in Classification
German Cancer Consortium (DKTK)（德国癌症联盟（DKTK））；German Cancer Research Center (DKFZ)（德国癌症研究中心（DKFZ））；Goethe University Frankfurt（法兰克福大学）；Inria（法国国家信息与自动化研究所）；Ecole Normale Supérieure（巴黎高等师范学院）；PSL Research University（巴黎文理研究大学）
Truthful Calibration Errors for Multi-Class Prediction
Peking University（北京大学）；Northwestern University（西北大学）；Microsoft Research, New England（微软研究院（新英格兰））；Northeastern University（东北大学）；Khoury College of Computer Sciences（计算机科学学院）
San Diego State University（圣地亚哥州立大学）；Perelman School of Medicine at the University of Pennsylvania（宾夕法尼亚大学佩雷尔曼医学院）；University of Pennsylvania（宾夕法尼亚大学）；Google（谷歌）；Helix
This paper investigates the post-hoc calibration of confidence for "exploratory" machine learning classification problems. The difficulty in these problems stems from the continuing desire to push the boundaries of which categories have enough examples to generalize from when curating datasets, and confusion regarding the validity of those categories. We argue that for such problems the "one-versus-all" approach (top-label calibration) must be used rather than the "calibrate-the-full-response-matrix" approach advocated elsewhere in the literature. We introduce and test four new algorithms desi…
In this paper, we study the classification problem by estimating the conditional probability function of the given data. Different from the traditional expected risk estimation theory on empirical data, we calculate the probability via Fredholm equation, this leads to estimate the distribution of the data. Based on the Fredholm equation, a new expected risk estimation theory by estimating the cumulative distribution function is presented. The main characteristics of the new expected risk estimation is to measure the risk on the distribution of the input space. The corresponding empirical risk …
Western Sydney University（西悉尼大学）；Ecole Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）
A multi-label classifier estimates the binary label state (relevant vs irrelevant) for each of a set of concept labels, for any given instance. Probabilistic multi-label classifiers provide a predictive posterior distribution over all possible labelset combinations of such label states (the powerset of labels) from which we can provide the best estimate, simply by selecting the labelset corresponding to the largest expected accuracy, over that distribution. For example, in maximizing exact match accuracy, we provide the mode of the distribution. But how does this relate to the confidence we ma…
We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we show that it is non-trivial to select a good estimator without knowledge about the distributions of the random variables. We investigate and bound the bias and variance of the aforementioned estimators and prove consistency. The variance of cross validation can be significantly reduced, but not without risking a large bias. The bias and variance of different va…
