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Generalized cross-validation (GCV) is a widely-used method for estimating the squared out-of-sample prediction risk that employs a scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this…

Statistics Theory · Mathematics 2024-04-23 Pierre C. Bellec , Jin-Hong Du , Takuya Koriyama , Pratik Patil , Kai Tan

There is increasing interest in the use of diagnostic rules based on microarray data. These rules are formed by considering the expression levels of thousands of genes in tissue samples taken on patients of known classification with respect…

Statistics Theory · Mathematics 2008-12-18 G. J. McLachlan , J. Chevelu , J. Zhu

K-fold Cross Validation is commonly used to evaluate classifiers and tune their hyperparameters. However, it assumes that data points are Independent and Identically Distributed (i.i.d.) so that samples used in the training and test sets…

Machine Learning · Computer Science 2019-04-10 Akbar Dehghani , Tristan Glatard , Emad Shihab

Test-time computation has become a primary driver of progress in large language model (LLM) reasoning, but it is increasingly bottlenecked by expensive verification. In many reasoning systems, a large fraction of verifier calls are spent on…

Artificial Intelligence · Computer Science 2026-02-05 Shuhui Qu

In conventional supervised classification, true labels are required for individual instances. However, it could be prohibitive to collect the true labels for individual instances, due to privacy concerns or unaffordable annotation costs.…

Machine Learning · Computer Science 2023-06-29 Zixi Wei , Lei Feng , Bo Han , Tongliang Liu , Gang Niu , Xiaofeng Zhu , Heng Tao Shen

Prediction error is critical to assessing the performance of statistical methods and selecting statistical models. We propose the cross-validation and approximated cross-validation methods for estimating prediction error under a broad…

Statistics Theory · Mathematics 2007-06-13 Jianqing Fan , Chunming Zhang

Learning ensembles by bagging can substantially improve the generalization performance of low-bias, high-variance estimators, including those evolved by Genetic Programming (GP). To be efficient, modern GP algorithms for evolving (bagging)…

Neural and Evolutionary Computing · Computer Science 2021-02-08 Marco Virgolin

Selective classification (or classification with a reject option) pairs a classifier with a selection function to determine whether or not a prediction should be accepted. This framework trades off coverage (probability of accepting a…

Machine Learning · Computer Science 2023-02-23 Andrea Pugnana , Salvatore Ruggieri

Test-time scaling is a powerful strategy for boosting the performance of large language models on complex reasoning tasks. While state-of-the-art approaches often employ generative verifiers to select the best solution from a pool of…

Artificial Intelligence · Computer Science 2025-10-17 Kyle Montgomery , Sijun Tan , Yuqi Chen , Siyuan Zhuang , Tianjun Zhang , Raluca Ada Popa , Chenguang Wang

A recent case study from AWS by Chong et al. proposes an effective methodology for Bounded Model Checking in industry. In this paper, we report on a follow up case study that explores the methodology from the perspective of three research…

Software Engineering · Computer Science 2021-07-05 Siddharth Priya , Xiang Zhou , Yusen Su , Yakir Vizel , Yuyan Bao , Arie Gurfinkel

Overfitting is the bane of data analysts, even when data are plentiful. Formal approaches to understanding this problem focus on statistical inference and generalization of individual analysis procedures. Yet the practice of data analysis…

Machine Learning · Computer Science 2015-09-28 Cynthia Dwork , Vitaly Feldman , Moritz Hardt , Toniann Pitassi , Omer Reingold , Aaron Roth

In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them(e.g., transitivity when describing preferences).…

Computer Science and Game Theory · Computer Science 2013-06-20 Ilan Nehama

Cross-validation (CV) is a popular method for model-selection. Unfortunately, it is not immediately obvious how to apply CV to unsupervised or exploratory contexts. This thesis discusses some extensions of cross-validation to unsupervised…

Methodology · Statistics 2009-09-17 Patrick O. Perry

We propose the holdout randomization test (HRT), an approach to feature selection using black box predictive models. The HRT is a specialized version of the conditional randomization test (CRT; Candes et al., 2018) that uses data splitting…

Methodology · Statistics 2021-03-23 Wesley Tansey , Victor Veitch , Haoran Zhang , Raul Rabadan , David M. Blei

Standard techniques such as leave-one-out cross-validation (LOOCV) might not be suitable for evaluating the predictive performance of models incorporating structured random effects. In such cases, the correlation between the training and…

Methodology · Statistics 2024-06-21 A. Adin , E. Krainski , A. Lenzi , Z. Liu , J. Martínez-Minaya , H. Rue

With the growing application of spatial predictive modeling in ecology, the question of how to appropriately evaluate the resulting maps has gained increasing attention. While there is consensus that map accuracy is ideally estimated using…

Methodology · Statistics 2026-05-14 Jan Linnenbrink , Jakub Nowosad , Hanna Meyer

We present CrowdHub, a tool for running systematic evaluations of task designs on top of crowdsourcing platforms. The goal is to support the evaluation process, avoiding potential experimental biases that, according to our empirical…

Human-Computer Interaction · Computer Science 2019-09-11 Jorge Ramírez , Simone Degiacomi , Davide Zanella , Marcos Baez , Fabio Casati , Boualem Benatallah

Group Relative Policy Optimization (GRPO), a prominent algorithm within the Reinforcement Learning from Verifiable Rewards (RLVR) framework, has achieved strong results in improving the reasoning capabilities of large language models…

Machine Learning · Computer Science 2026-05-21 Xixiang He , Qiyao Sun , Ao Cheng , Xingming Li , Xuanyu Ji , Hailun Lu , Runke Huang , Qingyong Hu

Multiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses, with relatively few true signals. In this paper, we consider the multiple testing problem where…

Methodology · Statistics 2016-06-28 Ang Li , Rina Foygel Barber

Selecting hyperparameters for unsupervised learning problems is challenging in general due to the lack of ground truth for validation. Despite the prevalence of this issue in statistics and machine learning, especially in clustering…

Machine Learning · Statistics 2020-02-04 Xinjie Fan , Yuguang Yue , Purnamrita Sarkar , Y. X. Rachel Wang