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The regression function is one of the key objects of binary classification, since it not only determines a Bayes optimal classifier, hence, defines an optimal decision boundary, but also encodes the conditional distribution of the output…

Machine Learning · Statistics 2025-06-03 Ambrus Tamás , Balázs Csanád Csáji

Hyperparameters greatly impact models' capabilities; however, modern models are too large for extensive search. Instead, researchers design recipes that train well across scales based on their understanding of the hyperparameters. Despite…

Machine Learning · Computer Science 2025-10-06 Nicholas Lourie , He He , Kyunghyun Cho

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…

Methodology · Statistics 2023-01-12 Zhipeng Lou , Xianyang Zhang , Wei Biao Wu

We propose a general framework for nonasymptotic covariance matrix estimation making use of concentration inequality-based confidence sets. We specify this framework for the estimation of large sparse covariance matrices through…

Methodology · Statistics 2020-12-17 Adam B Kashlak , Linglong Kong

We consider statistical inference in high-dimensional regression problems under affine constraints on the parameter space. The theoretical study of this is motivated by the study of genetic determinants of diseases, such as diabetes, using…

We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…

Machine Learning · Statistics 2016-11-17 Mohammad Hossein Rohban , Prakash Ishwar , Birant Orten , William C. Karl , Venkatesh Saligrama

The problem of constructing a simultaneous confidence surface for the 2-dimensional mean function of a non-stationary functional time series is challenging as these bands can not be built on classical limit theory for the maximum absolute…

Statistics Theory · Mathematics 2024-11-27 Holger Dette , Weichi Wu

In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…

Statistics Theory · Mathematics 2019-01-14 Anupam Kundu , Subir Kumar Bhandari

We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete…

Machine Learning · Statistics 2015-11-24 Yang Ning , Tianqi Zhao , Han Liu

This article conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix…

Machine Learning · Statistics 2024-02-22 Victor Leger , Romain Couillet

We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…

Statistics Theory · Mathematics 2021-03-22 Eftychia Solea , Holger Dette

Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…

Methodology · Statistics 2018-12-21 Jinyuan Chang , Yumou Qiu , Qiwei Yao , Tao Zou

We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…

Statistics Theory · Mathematics 2017-05-09 Taras Bodnar , Stepan Mazur , Edward Ngailo , Nestor Parolya

Bootstrapping is often applied to get confidence limits for semiparametric inference of a target parameter in the presence of nuisance parameters. Bootstrapping with replacement can be computationally expensive and problematic when…

This paper gives a general method for deriving limiting distributions of complete case statistics for missing data models from corresponding results for the model where all data are observed. This provides a convenient tool for obtaining…

Statistics Theory · Mathematics 2013-02-20 Hira L. Koul , Ursula U. Müller , Anton Schick

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…

Statistics Theory · Mathematics 2022-09-28 Wenlong Mou , Martin J. Wainwright , Peter L. Bartlett

Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g.,…

Statistics Theory · Mathematics 2025-10-14 Pau Batlle , Pratik Patil , Michael Stanley , Javier Ruiz Lupon , Houman Owhadi , Mikael Kuusela

Likelihood-free inference for simulator-based statistical models has recently attracted a surge of interest, both in the machine learning and statistics communities. The primary focus of these research fields has been to approximate the…

Methodology · Statistics 2022-05-27 Jukka Corander , Ulpu Remes , Ida Holopainen , Timo Koski

We provide exact asymptotic expressions for the performance of regression by an $L-$layer deep random feature (RF) model, where the input is mapped through multiple random embedding and non-linear activation functions. For this purpose, we…

Machine Learning · Statistics 2023-02-14 David Bosch , Ashkan Panahi , Babak Hassibi

Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…

Machine Learning · Statistics 2017-09-07 Daniel Ting , Eric Brochu