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Inspired by the concept of active learning, we propose active inference$\unicode{x2013}$a methodology for statistical inference with machine-learning-assisted data collection. Assuming a budget on the number of labels that can be collected,…

Machine Learning · Statistics 2026-04-09 Tijana Zrnic , Emmanuel J. Candès

In modern data analysis, it is common to use machine learning methods to predict outcomes on unlabeled datasets and then use these pseudo-outcomes in subsequent statistical inference. Inference in this setting is often called…

Methodology · Statistics 2024-11-04 Feng Gan , Wanfeng Liang , Changliang Zou

Active statistical inference is a new method for inference with AI-assisted data collection. Given a budget on the number of labeled data points that can be collected and assuming access to an AI predictive model, the basic idea is to…

Machine Learning · Statistics 2025-11-13 Puheng Li , Tijana Zrnic , Emmanuel Candès

Construction of valid statistical inference for estimators based on data-driven selection has received a lot of attention in the recent times. Berk et al. (2013) is possibly the first work to provide valid inference for Gaussian…

This work addresses the problem of conducting valid inference for additive and linear mixed models after model selection. One possible solution to overcome overconfident inference results after model selection is selective inference, which…

Methodology · Statistics 2020-12-22 David Rügamer , Philipp F. M. Baumann , Sonja Greven

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple…

Machine Learning · Computer Science 2016-03-03 Cynthia Dwork , Vitaly Feldman , Moritz Hardt , Toniann Pitassi , Omer Reingold , Aaron Roth

Estimating how well a machine learning model performs during inference is critical in a variety of scenarios (for example, to quantify uncertainty, or to choose from a library of available models). However, the standard accuracy estimate of…

Computer Vision and Pattern Recognition · Computer Science 2021-10-07 Xuechen Zhang , Samet Oymak , Jiasi Chen

It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees that classical statistical theory provides…

Statistics Theory · Mathematics 2013-06-06 Richard Berk , Lawrence Brown , Andreas Buja , Kai Zhang , Linda Zhao

We develop a general approach to valid inference after model selection. At the core of our framework is a result that characterizes the distribution of a post-selection estimator conditioned on the selection event. We specialize the…

Statistics Theory · Mathematics 2016-05-04 Jason D. Lee , Dennis L. Sun , Yuekai Sun , Jonathan E. Taylor

Predictive variability due to data ambiguities has typically been addressed via construction of dedicated models with built-in probabilistic capabilities that are trained to predict uncertainty estimates as variables of interest. These…

Machine Learning · Computer Science 2023-08-04 Katarína Tóthová , Ľubor Ladický , Daniel Thul , Marc Pollefeys , Ender Konukoglu

Simulation-based calibration checking (SBC) refers to the validation of an inference algorithm and model implementation through repeated inference on data simulated from a generative model. In the original and commonly used approach, the…

Methodology · Statistics 2025-03-11 Teemu Säilynoja , Marvin Schmitt , Paul-Christian Bürkner , Aki Vehtari

Adaptive experiments use preliminary analyses of the data to inform further course of action and are commonly used in many disciplines including medical and social sciences. Because the null hypothesis and experimental design are…

Methodology · Statistics 2026-05-26 Tobias Freidling , Qingyuan Zhao , Zijun Gao

Subsampling is commonly used to mitigate costs associated with data acquisition, such as time or energy requirements, motivating the development of algorithms for estimating the fully-sampled signal of interest $x$ from partially observed…

Machine Learning · Computer Science 2025-04-23 Oisin Nolan , Tristan S. W. Stevens , Wessel L. van Nierop , Ruud J. G. van Sloun

Uncertainty quantification is critical in safety-sensitive applications but is often omitted from off-the-shelf neural networks due to adverse effects on predictive performance. Retrofitting uncertainty estimates post-hoc typically requires…

Machine Learning · Computer Science 2025-06-03 Lennart Bramlage , Cristóbal Curio

We develop methodology for valid inference after variable selection in logistic regression when the responses are partially observed, that is, when one observes a set of error-prone testing outcomes instead of the true values of the…

Methodology · Statistics 2025-04-17 Qinyan Shen , Karl Gregory , Xianzheng Huang

Complex survey data are usually collected following complex sampling designs. Accounting for the sampling design is essential to obtain unbiased estimates and valid inferences when analyzing complex survey data. The area under the receiver…

Methodology · Statistics 2026-03-31 Amaia Iparragirre , Thomas Lumley , Irantzu Barrio

We develop methods for forming prediction sets in an online setting where the data generating distribution is allowed to vary over time in an unknown fashion. Our framework builds on ideas from conformal inference to provide a general…

Methodology · Statistics 2021-12-10 Isaac Gibbs , Emmanuel Candès

This technical note considers the sampling of outcomes that provide the greatest amount of information about the structure of underlying world models. This generalisation furnishes a principled approach to structure learning under a…

Neurons and Cognition · Quantitative Biology 2025-12-25 Karl Friston , Lancelot Da Costa , Alexander Tschantz , Conor Heins , Christopher Buckley , Tim Verbelen , Thomas Parr

When the target of statistical inference is chosen in a data-driven manner, the guarantees provided by classical theories vanish. We propose a solution to the problem of inference after selection by building on the framework of algorithmic…

Statistics Theory · Mathematics 2022-03-16 Tijana Zrnic , Michael I. Jordan

Post-selection inference consists in providing statistical guarantees, based on a data set, that are robust to a prior model selection step on the same data set. In this paper, we address an instance of the post-selection-inference problem,…

Statistics Theory · Mathematics 2025-06-16 Dominique Bontemps , François Bachoc , Pierre Neuvial
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