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This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…

Statistics Theory · Mathematics 2019-03-18 Dominique Dehay , Khalil El Waled , Vincent Monsan

The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical…

Methodology · Statistics 2022-10-28 Ziang Niu , Yuwen Gu , Wei Li

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…

Statistics Theory · Mathematics 2020-07-27 T. Tony Cai , Tengyuan Liang , Alexander Rakhlin

We consider a model where a signal (discrete or continuous) is observed with an additive Gaussian noise process. The signal is issued from a linear combination of a finite but increasing number of translated features. The features are…

Statistics Theory · Mathematics 2024-07-23 Cristina Butucea , Jean-François Delmas , Anne Dutfoy , Clément Hardy

The multi-index model is a simple yet powerful high-dimensional regression model which circumvents the curse of dimensionality assuming $ \mathbb{E} [ Y | X ] = g(A^\top X) $ for some unknown index space $A$ and link function $g$. In this…

Statistics Theory · Mathematics 2020-06-04 Timo Klock , Alessandro Lanteri , Stefano Vigogna

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…

Information Theory · Computer Science 2017-04-19 Sajad Daei , Farzan Haddadi

We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…

Machine Learning · Statistics 2025-03-11 Gilles Blanchard , Jean-Baptiste Fermanian , Hannah Marienwald

The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…

Methodology · Statistics 2012-11-05 Cun-Hui Zhang , Stephanie S. Zhang

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Statistics Theory · Mathematics 2025-11-25 Sayantan Banerjee , Ismaël Castillo , Subhashis Ghosal

In this paper, we aim to estimate the direction of an underlying signal from its nonlinear observations following the semi-parametric single index model (SIM). Unlike conventional compressed sensing where the signal is assumed to be sparse,…

Machine Learning · Computer Science 2022-06-02 Jiulong Liu , Zhaoqiang Liu

This paper addresses the problem of detecting multidimensional subspace signals, which model range-spread targets, in noise of unknown covariance. It is assumed that a primary channel of measurements, possibly consisting of signal plus…

Signal Processing · Electrical Eng. & Systems 2022-10-04 Danilo Orlando , Giuseppe Ricci , Louis L. Scharf

A good classification method should yield more accurate results than simple heuristics. But there are classification problems, especially high-dimensional ones like the ones based on image/video data, for which simple heuristics can work…

Machine Learning · Statistics 2018-06-15 Tarun Yellamraju , Jonas Hepp , Mireille Boutin

We study the problem of estimation and testing in logistic regression with class-conditional noise in the observed labels, which has an important implication in the Positive-Unlabeled (PU) learning setting. With the key observation that the…

Methodology · Statistics 2020-08-14 Hyebin Song , Ran Dai , Garvesh Raskutti , Rina Foygel Barber

Recently emerging large-scale biomedical data pose exciting opportunities for scientific discoveries. However, the ultrahigh dimensionality and non-negligible measurement errors in the data may create difficulties in estimation. There are…

Methodology · Statistics 2022-10-28 Xin Ma , Suprateek Kundu

The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…

Statistics Theory · Mathematics 2021-03-02 Hamid Eftekhari , Moulinath Banerjee , Ya'acov Ritov

This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge…

Statistics Theory · Mathematics 2020-06-02 Martin Genzel , Alexander Stollenwerk

In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…

Statistics Theory · Mathematics 2022-07-20 Paavo Sattler , Markus Pauly

Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a…

Methodology · Statistics 2020-09-28 Satyajit Ghosh , Zhiqiang Tan

This paper provides theoretical insights into high-dimensional binary classification with class-conditional noisy labels. Specifically, we study the behavior of a linear classifier with a label noisiness aware loss function, when both the…

Machine Learning · Computer Science 2024-05-24 Aymane El Firdoussi , Mohamed El Amine Seddik

It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…

Machine Learning · Statistics 2025-07-21 James A. D. Binnie , Paweł Dłotko , John Harvey , Jakub Malinowski , Ka Man Yim