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Related papers: On adaptive inference and confidence bands

200 papers

The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymptotically optimal in order at a growing number of observation on any regular subspace…

Probability · Mathematics 2007-05-23 Eugene Ostrovsky , Leonid Sirota

We investigate the problem of constructing Bayesian credible sets that are honest and adaptive for the L2-loss over a scale of Sobolev classes with regularity ranging between [D; 2D], for some given D in the context of the…

Statistics Theory · Mathematics 2014-04-24 Botond Szabo , Aad van der Vaart , Harry van Zanten

We study confidence intervals based on hard-thresholding, soft-thresholding, and adaptive soft-thresholding in a linear regression model where the number of regressors $k$ may depend on and diverge with sample size $n$. In addition to the…

Statistics Theory · Mathematics 2018-10-08 Ulrike Schneider

Deep learning models have significantly improved prediction accuracy in various fields, gaining recognition across numerous disciplines. Yet, an aspect of deep learning that remains insufficiently addressed is the assessment of prediction…

Machine Learning · Statistics 2024-12-18 Asaf Ben Arie , Malka Gorfine

Adaptive experiments such as multi-arm bandits adapt the treatment-allocation policy and/or the decision to stop the experiment to the data observed so far. This has the potential to improve outcomes for study participants within the…

Methodology · Statistics 2024-05-03 Aurélien Bibaut , Nathan Kallus

To answer questions of "causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is…

Methodology · Statistics 2025-04-14 Ping Zhang , Ruoyu Wang , Wang Miao

This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…

Statistics Theory · Mathematics 2025-06-05 Yuetian Luo , Chao Gao

Functional Data Analysis represents a field of growing interest in statistics. Despite several studies have been proposed leading to fundamental results, the problem of obtaining valid and efficient prediction sets has not been thoroughly…

Methodology · Statistics 2021-04-13 Jacopo Diquigiovanni , Matteo Fontana , Simone Vantini

The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level…

Methodology · Statistics 2021-07-30 Kun Zhou , Ker-Chau Li , Qing Zhou

We propose a novel technique for analyzing adaptive sampling called the {\em Simulator}. Our approach differs from the existing methods by considering not how much information could be gathered by any fixed sampling strategy, but how…

Machine Learning · Computer Science 2023-04-25 Max Simchowitz , Kevin Jamieson , Benjamin Recht

Predictive models make mistakes. Hence, there is a need to quantify the uncertainty associated with their predictions. Conformal inference has emerged as a powerful tool to create statistically valid prediction regions around point…

Machine Learning · Statistics 2024-02-14 Luben M. C. Cabezas , Mateus P. Otto , Rafael Izbicki , Rafael B. Stern

Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in…

Statistics Theory · Mathematics 2013-05-27 T. Tony Cai , Mark G. Low , Yin Xia

Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…

Machine Learning · Statistics 2012-03-21 Robert Hable

To make informative public policy decisions in battling the ongoing COVID-19 pandemic, it is important to know the disease prevalence in a population. There are two intertwined difficulties in estimating this prevalence based on testing…

Methodology · Statistics 2020-12-01 Bryan Cai , John P. A. Ioannidis , Eran Bendavid , Lu Tian

Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…

Methodology · Statistics 2014-04-03 Adel Javanmard , Andrea Montanari

We study the problem of learning a high-density region of an arbitrary distribution over $\mathbb{R}^d$. Given a target coverage parameter $\delta$, and sample access to an arbitrary distribution $D$, we want to output a confidence set $S…

Data Structures and Algorithms · Computer Science 2025-05-14 Chao Gao , Liren Shan , Vaidehi Srinivas , Aravindan Vijayaraghavan

In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a…

Methodology · Statistics 2019-06-06 Gang Cheng , Yen-Chi Chen

Quantifying uncertainty using confidence regions is a central goal of statistical inference. Despite this, methodologies for confidence bands in Functional Data Analysis are still underdeveloped compared to estimation and hypothesis…

Methodology · Statistics 2022-11-14 Dominik Liebl , Matthew Reimherr

The choice of hyperparameters greatly impacts performance in natural language processing. Often, it is hard to tell if a method is better than another or just better tuned. Tuning curves fix this ambiguity by accounting for tuning effort.…

Computation and Language · Computer Science 2024-04-10 Nicholas Lourie , Kyunghyun Cho , He He

This paper is concerned with inference in threshold regression models when the practitioners do not know whether at the threshold point the true specification has a kink or a jump. We nest previous works that assume either continuity or…

Statistics Theory · Mathematics 2020-01-15 Javier Hidalgo , Jungyoon Lee , Myung Hwan Seo