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Machine learning applications often require calibrated predictions, e.g. a 90\% credible interval should contain the true outcome 90\% of the times. However, typical definitions of calibration only require this to hold on average, and offer…

Machine Learning · Statistics 2020-09-10 Shengjia Zhao , Tengyu Ma , Stefano Ermon

Clustering is a well-studied unsupervised learning task that aims to partition data points into a number of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV…

Optimization and Control · Mathematics 2025-09-25 Connor Lawless , Oktay Gunluk

Fairness researchers in machine learning (ML) have coalesced around several fairness criteria which provide formal definitions of what it means for an ML model to be fair. However, these criteria have some serious limitations. We identify…

Machine Learning · Computer Science 2022-07-14 Liam Peet-Pare , Nidhi Hegde , Alona Fyshe

Uncertainty is a fundamental aspect of real-world scenarios, where perfect information is rarely available. Humans naturally develop complex internal models to navigate incomplete data and effectively respond to unforeseen or partially…

Machine Learning · Computer Science 2025-08-08 Wenhao Liang , Chang Dong , Liangwei Zheng , Wei Zhang , Weitong Chen

A main puzzle of deep neural networks (DNNs) revolves around the apparent absence of "overfitting", defined in this paper as follows: the expected error does not get worse when increasing the number of neurons or of iterations of gradient…

Machine Learning · Computer Science 2018-07-02 Tomaso Poggio , Qianli Liao , Brando Miranda , Andrzej Banburski , Xavier Boix , Jack Hidary

This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline…

Statistics Theory · Mathematics 2011-09-15 Sylvain Arlot , Francis Bach

We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating…

Machine Learning · Computer Science 2022-10-03 Anastasios N. Angelopoulos , Stephen Bates , Emmanuel J. Candès , Michael I. Jordan , Lihua Lei

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…

Machine Learning · Computer Science 2020-02-28 Jonathan Wenger , Hedvig Kjellström , Rudolph Triebel

Pruning and quantization techniques have been broadly successful in reducing the number of parameters needed for large neural networks, yet theoretical justification for their empirical success falls short. We consider a randomized greedy…

Machine Learning · Computer Science 2025-12-09 Houssam El Cheairi , David Gamarnik , Rahul Mazumder

As the use of predictive machine learning algorithms increases in high-stakes decision-making, it is imperative that these algorithms are fair across sensitive groups. However, measuring and enforcing fairness in real-world applications can…

Machine Learning · Statistics 2025-07-14 Beepul Bharti , Mary Versa Clemens-Sewall , Paul H. Yi , Jeremias Sulam

This study introduces the Misclassification Likelihood Matrix (MLM) as a novel tool for quantifying the reliability of neural network predictions under distribution shifts. The MLM is obtained by leveraging softmax outputs and clustering…

Ensuring that classifiers are well-calibrated, i.e., their predictions align with observed frequencies, is a minimal and fundamental requirement for classifiers to be viewed as trustworthy. Existing methods for assessing multiclass…

Machine Learning · Computer Science 2025-10-30 Mahmoud Hegazy , Michael I. Jordan , Aymeric Dieuleveut

Although deep neural networks (DNNs) achieve high predictive accuracy, their confidence estimates are often unreliable, potentially compromising user trust in their decisions. This has motivated research on calibrated models, where…

Machine Learning · Computer Science 2026-05-25 Ramya Hebbalaguppe , Ajay Shastry , Soumya Suvra Ghosal , Chetan Arora

We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically…

Machine Learning · Statistics 2018-12-05 Gamaleldin F. Elsayed , Dilip Krishnan , Hossein Mobahi , Kevin Regan , Samy Bengio

Predictors map individual instances in a population to the interval $[0,1]$. For a collection $\mathcal C$ of subsets of a population, a predictor is multi-calibrated with respect to $\mathcal C$ if it is simultaneously calibrated on each…

Machine Learning · Computer Science 2021-11-18 Maya Burhanpurkar , Zhun Deng , Cynthia Dwork , Linjun Zhang

Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given…

Machine Learning · Computer Science 2023-06-27 Jamelle Watson-Daniels , David C. Parkes , Berk Ustun

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.…

Machine Learning · Statistics 2021-12-08 Tianyang Hu , Jun Wang , Wenjia Wang , Zhenguo Li

Deep neural networks have demonstrated remarkable performance across numerous learning tasks but often suffer from miscalibration, resulting in unreliable probability outputs. This has inspired many recent works on mitigating…

Machine Learning · Computer Science 2025-09-23 Wenjian Huang , Guiping Cao , Jiahao Xia , Jingkun Chen , Hao Wang , Jianguo Zhang

We consider the problem of constructing probabilistic predictions that lead to accurate decisions when employed by downstream users to inform actions. For a single decision maker, designing an optimal predictor is equivalent to minimizing a…

Machine Learning · Computer Science 2025-10-15 Isaac Gibbs , Ryan J. Tibshirani

In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores…

Machine Learning · Computer Science 2023-05-24 Francesco Marchetti , Sabrina Guastavino , Cristina Campi , Federico Benvenuto , Michele Piana
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