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High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint…

Machine Learning · Statistics 2023-06-13 Kartheek Bondugula , Santiago Mazuelas , Aritz Pérez

This article concerns the performance limits of strictly causal state estimation for linear systems with fixed, but uncertain, parameters belonging to a finite set. In particular, we provide upper and lower bounds on the smallest achievable…

Optimization and Control · Mathematics 2024-03-29 Olle Kjellqvist

Parameter fitting of data to a proposed equation almost always consider these parameters as independent variables. Here, the method proposed optimizes an arbitrary number of variables by the minimization of a function of a single variable.…

Chemical Physics · Physics 2010-06-15 Christopher G. Jesudason

We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the…

Machine Learning · Statistics 2011-05-25 Jean-Yves Audibert , Sebastien Bubeck , Gabor Lugosi

We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…

Optimization and Control · Mathematics 2024-06-04 Jochen Schmid , Philipp Seufert , Michael Bortz

We explore the minimax optimal error associated with a demographic parity-constrained regression problem within the context of a linear model. Our proposed model encompasses a broader range of discriminatory bias sources compared to the…

Statistics Theory · Mathematics 2023-08-25 Kazuto Fukuchi , Jun Sakuma

A least product relative error criterion is proposed for multiplicative regression models. It is invariant under scale transformation of the outcome and covariates. In addition, the objective function is smooth and convex, resulting in a…

Methodology · Statistics 2013-09-03 Kani Chen , Yuanyuan Lin , Zhanfeng Wang , Zhiliang Ying

We present a computational motivation for restricted maximum likelihood (REML) estimation in linear mixed models using an expectation--maximization (EM) algorithm. At each iteration, maximum likelihood (ML) and REML solve the same…

Computation · Statistics 2026-02-11 Andrew T. Karl

In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…

Statistics Theory · Mathematics 2017-07-18 Yiyuan She , Kun Chen

In a seminal paper \cite{studden1968} characterized $c$-optimal designs in regression models, where the regression functions form a Chebyshev system. He used these results to determine the optimal design for estimating the individual…

Statistics Theory · Mathematics 2019-06-21 Holger Dette , Viatcheslav B. Melas , Petr Shpilev

Application of the minimum distance method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally…

Computation · Statistics 2017-02-15 Jiwoong Kim

We present an optimization problem emerging from optimal control theory and situated at the intersection of fractional programming and linear max-min programming on polytopes. A na\"ive solution would require solving four nested, possibly…

Optimization and Control · Mathematics 2021-11-19 Jean-Baptiste Bouvier , Melkior Ornik

A general theory for Gaussian mean estimation that automatically adapts to unknown sparsity under arbitrary norms is proposed. The theory is applied to produce adaptively minimax rate-optimal estimators in high dimensional regression and…

Statistics Theory · Mathematics 2015-12-01 Sourav Chatterjee

We develop a unified theory of designs for controlled experiments that balance baseline covariates a priori (before treatment and before randomization) using the framework of minimax variance and a new method called kernel allocation. We…

Statistics Theory · Mathematics 2017-08-02 Nathan Kallus

In randomized controlled trials without interference, regression adjustment is widely used to enhance the efficiency of treatment effect estimation. This paper extends this efficiency principle to settings with network interference, where a…

Methodology · Statistics 2025-02-18 Xinyuan Fan , Chenlei Leng , Weichi Wu

We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to…

Statistics Theory · Mathematics 2021-01-15 Kirsten Schorning , Holger Dette

We consider a general nonparametric regression model called the compound model. It includes, as special cases, sparse additive regression and nonparametric (or linear) regression with many covariates but possibly a small number of relevant…

Statistics Theory · Mathematics 2013-01-04 Arnak Dalalyan , Yuri Ingster , Alexandre Tsybakov

We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure,…

Methodology · Statistics 2025-07-25 Joyee Ghosh , Xun Li

We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the…

Computation · Statistics 2020-01-29 HaiYing Wang , Yanyuan Ma

We have established the association matrix that expresses the estimator of effects under baseline parameterization, which has been considered in some recent literature, in an equivalent form as a linear combination of estimators of effects…

Methodology · Statistics 2024-09-04 Xietao Zhou , Steven G. Gilmour