Tootfinder

Least squares-based methods to bias adjustment in scalar-on-function regression model using a functional instrumental variable
Xiwei Chen, Ufuk Beyaztas, Caihong Qin, Heyang Ji, Gilson Honvoh, Roger S. Zoh, Lan Xue, Carmen D. Tekwe
https://arxiv.org/abs/2509.12122

Least squares-based methods to bias adjustment in scalar-on-function regression model using a functional instrumental variable
Instrumental variables are widely used to adjust for measurement error bias when assessing associations of health outcomes with ME prone independent variables. IV approaches addressing ME in longitudinal models are well established, but few methods exist for functional regression. We develop two methods to adjust for ME bias in scalar on function linear models. We regress a scalar outcome on an ME prone functional variable using a functional IV for model identification and propose two least squ…

Efficient Group Lasso Regularized Rank Regression with Data-Driven Parameter Determination
Meixia Lin, Meijiao Shi, Yunhai Xiao, Qian Zhang
https://arxiv.org/abs/2510.11546 http…

Efficient Group Lasso Regularized Rank Regression with Data-Driven Parameter Determination
High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective and incorporate structured group sparsity regularization, a natural generalization of the lasso, yielding a group lasso regularized rank regression method. By extending the tuning-free parameter selection scheme originally developed for the lasso, we introduce …

Entropy and Learning of Lipschitz Functions under Log-Concave Measures
Pierre Bizeul, Boaz Klartag
https://arxiv.org/abs/2509.10355 https://arxiv.org/pdf/2…

Entropy and Learning of Lipschitz Functions under Log-Concave Measures
We study regression of $1$-Lipschitz functions under a log-concave measure $μ$ on $\mathbb{R}^d$. We focus on the high-dimensional regime where the sample size $n$ is subexponential in $d$, in which distribution-free estimators are ineffective. We analyze two polynomial-based procedures: the projection estimator, which relies on knowledge of an orthogonal polynomial basis of $μ$, and the least-squares estimator over low-degree polynomials, which requires no knowledge of $μ$ whatsoever. Their…

Comparing Building Thermal Dynamics Models and Estimation Methods for Grid-Edge Applications
Ninad Gaikwad, Kunal Shankar, Anamika Dubey, Alan Love, Olvar Bergland
https://arxiv.org/abs/2508.09118

Comparing Building Thermal Dynamics Models and Estimation Methods for Grid-Edge Applications
We need computationally efficient and accurate building thermal dynamics models for use in grid-edge applications. This work evaluates two grey-box approaches for modeling building thermal dynamics: RC-network models and structured regression models. For RC-network models, we compare parameter estimation methods including Nonlinear Least Squares, Batch Estimation, and Maximum Likelihood Estimation. We use the Almon Lag Structure with Linear Least Squares for estimating the structured regression…

Improved $\ell_{p}$ Regression via Iteratively Reweighted Least Squares
Alina Ene, Ta Duy Nguyen, Adrian Vladu
https://arxiv.org/abs/2510.01729 https://arx…

Improved $\ell_{p}$ Regression via Iteratively Reweighted Least Squares
We introduce fast algorithms for solving $\ell_{p}$ regression problems using the iteratively reweighted least squares (IRLS) method. Our approach achieves state-of-the-art iteration complexity, outperforming the IRLS algorithm by Adil-Peng-Sachdeva (NeurIPS 2019) and matching the theoretical bounds established by the complex algorithm of Adil-Kyng-Peng-Sachdeva (SODA 2019, J. ACM 2024) via a simpler lightweight iterative scheme. This bridges the existing gap between theoretical and practical a…

Enhancing Differentially Private Linear Regression via Public Second-Moment
Zilong Cao (The School of Mathematics, Northwest University), Hai Zhang (The School of Mathematics, Northwest University)
https://arxiv.org/abs/2508.18037

Enhancing Differentially Private Linear Regression via Public Second-Moment
Leveraging information from public data has become increasingly crucial in enhancing the utility of differentially private (DP) methods. Traditional DP approaches often require adding noise based solely on private data, which can significantly degrade utility. In this paper, we address this limitation in the context of the ordinary least squares estimator (OLSE) of linear regression based on sufficient statistics perturbation (SSP) under the unbounded data assumption. We propose a novel method …

Comparison of Gaussian process regression, partial least squares, random forest and support vector machines for a near infrared calibration of paracetamol samples
Aminata Sow, Issiaka Traore, Tidiane Diallo, Mohamed Traore, Abdramane Ba
https://arxiv.org/abs/2510.01064

Comparison of Gaussian process regression, partial least squares, random forest and support vector machines for a near infrared calibration of paracetamol samples
In this article, we analyze the near-infrared (NIR) spectra of fifty-eight (58) commercial tablets of 500 mg of paracetamol from different origins (that is, with different batch numbers) in the local markets in Bamako. The NIR spectra were recorded in the spectral range 930 nm-1700 nm. The samples are divided into forty-eight (48) samples forming the set of calibration (training set) and ten (10) samples used as the validation or test set. To perform multivariate calibration, we apply-three non…

A bias test for heteroscedastic linear least-squares regression
Eric Blankmeyer
https://arxiv.org/abs/2508.15969 https://arxiv.org/pdf/2508.15969

A bias test for heteroscedastic linear least-squares regression
Linear least squares regression is subject to bias due to an omitted variable, a mismeasured regressor, or simultaneity. A simple test to detect the bias is proposed and explored in simulation and in real data sets.

Quantum Communication Complexity of L2-Regularized Linear Regression Protocols
Sayaki Matsushita
https://arxiv.org/abs/2508.16141 https://arxiv.org/pdf/250…

Quantum Communication Complexity of L2-Regularized Linear Regression Protocols
Linear regression is fundamental to statistical analysis and machine learning, but its application to large-scale datasets necessitates distributed computing. The problem also arises in quantum computing, where handling extensive data requires distributed approaches. This paper investigates distributed linear regression in the quantum coordinator model. Building upon the distributed quantum least squares protocol developed by Montanaro and Shao, we propose improved and extended quantum protocol…

Sensitivity of weighted least squares estimators to omitted variables
Leonard Wainstein, Chad Hazlett
https://arxiv.org/abs/2508.02954 https://arxiv.org/pd…

Sensitivity of weighted least squares estimators to omitted variables
This paper introduces tools for assessing the sensitivity, to unobserved confounding, of a common estimator of the causal effect of a treatment on an outcome that employs weights: the weighted linear regression of the outcome on the treatment and observed covariates. We demonstrate through the omitted variable bias framework that the bias of this estimator is a function of two intuitive sensitivity parameters: (i) the proportion of weighted variance in the treatment that unobserved confounding …

Differentially Private Two-Stage Gradient Descent for Instrumental Variable Regression
Haodong Liang, Yanhao Jin, Krishnakumar Balasubramanian, Lifeng Lai
https://arxiv.org/abs/2509.22794

Differentially Private Two-Stage Gradient Descent for Instrumental Variable Regression
We study instrumental variable regression (IVaR) under differential privacy constraints. Classical IVaR methods (like two-stage least squares regression) rely on solving moment equations that directly use sensitive covariates and instruments, creating significant risks of privacy leakage and posing challenges in designing algorithms that are both statistically efficient and differentially private. We propose a noisy two-state gradient descent algorithm that ensures $ρ$-zero-concentrated differ…

A mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs
Shuixin Fang, Changtao Sheng, Bihao Su, Tao Zhou
https://arxiv.org/abs/2510.02635

A mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs
We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed method is built upon four essential components: (i) a martingale formulation of the forward backward stochastic differential equation (FBSDE); (ii) a small scale stochastic particle method for local linear regression (LLR); (iii) a decoupling strategy with a matrix-free solver for the weighted least-squares system us…

A Weighted Regression Approach to Break-Point Detection in Panel Data
Charl Pretorius, Heinrich Roodt
https://arxiv.org/abs/2510.00598 https://arxiv.org/pd…

A Weighted Regression Approach to Break-Point Detection in Panel Data
New procedures for detecting a change in the cross-sectional mean of panel data are proposed. The procedures rely on estimating nuisance parameters using certain cross-sectional means across panels using a weighted least squares regression. In the case of weak cross-sectional dependence between panels, we show how test statistics can be constructed to have a limit null distribution not depending on any choice of bandwidths typically needed to estimate the long-run variances of the panel errors.…

High-Dimensional Matrix-Variate Diffusion Index Models for Time Series Forecasting
Zhiren Ma, Qian Zhao, Riquan Zhang, Zhaoxing Gao
https://arxiv.org/abs/2508.04259 https://

High-Dimensional Matrix-Variate Diffusion Index Models for Time Series Forecasting
This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $α$-PCA method to extract low-dimensional matrix factors and build a bilinear regression linking future outcomes to these factors, estimated via iterative least squares. To handle weak factor structures, we introduce a supervised screening step to select informative rows and columns. Theoretical properties, including consistency and asymptotic normality,…

Incorporating priors in learning: a random matrix study under a teacher-student framework
Malik Tiomoko, Ekkehard Schnoor
https://arxiv.org/abs/2509.22124 https://

Incorporating priors in learning: a random matrix study under a teacher-student framework
Regularized linear regression is central to machine learning, yet its high-dimensional behavior with informative priors remains poorly understood. We provide the first exact asymptotic characterization of training and test risks for maximum a posteriori (MAP) regression with Gaussian priors centered at a domain-informed initialization. Our framework unifies ridge regression, least squares, and prior-informed estimators, and -- using random matrix theory -- yields closed-form risk formulas that …

Faster Linear Algebra Algorithms with Structured Random Matrices
Chris Cama\~no, Ethan N. Epperly, Raphael A. Meyer, Joel A. Tropp
https://arxiv.org/abs/2508.21189 https://

Faster Linear Algebra Algorithms with Structured Random Matrices
To achieve the greatest possible speed, practitioners regularly implement randomized algorithms for low-rank approximation and least-squares regression with structured dimension reduction maps. Despite significant research effort, basic questions remain about the design and analysis of randomized linear algebra algorithms that employ structured random matrices. This paper develops a new perspective on structured dimension reduction, based on the oblivious subspace injection (OSI) property. Th…

Core-elements Subsampling for Alternating Least Squares
Dunyao Xue, Mengyu Li, Cheng Meng, Jingyi Zhang
https://arxiv.org/abs/2509.18024 https://arxiv.org/…

Core-elements Subsampling for Alternating Least Squares
In this paper, we propose a novel element-wise subset selection method for the alternating least squares (ALS) algorithm, focusing on low-rank matrix factorization involving matrices with missing values, as commonly encountered in recommender systems. While ALS is widely used for providing personalized recommendations based on user-item interaction data, its high computational cost, stemming from repeated regression operations, poses significant challenges for large-scale datasets. To enhance t…

The Impact of AI Adoption on Retail Across Countries and Industries
Yunqi Liu
https://arxiv.org/abs/2509.15885 https://arxiv.org/pdf/2509.15885

The Impact of AI Adoption on Retail Across Countries and Industries
This study investigates the impact of artificial intelligence (AI) adoption on job loss rates using the Global AI Content Impact Dataset (2020--2025). The panel comprises 200 industry-country-year observations across Australia, China, France, Japan, and the United Kingdom in ten industries. A three-stage ordinary least squares (OLS) framework is applied. First, a full-sample regression finds no significant linear association between AI adoption rate and job loss rate ($β\approx -0.0026$, $p = …

Generalisation and benign over-fitting for linear regression onto random functional covariates
Andrew Jones, Nick Whiteley
https://arxiv.org/abs/2508.13895 https://

Generalisation and benign over-fitting for linear regression onto random functional covariates
We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved locations, subject to additive noise. This leads us away from the standard assumption of i.i.d. data to a setting in which the $n$ covariate vectors are exchangeable but not independent in general. Under an assumption of independence across dimensions, $4$-th…

Leveraging Covariates in Regression Discontinuity Designs
Matias D. Cattaneo, Filippo Palomba
https://arxiv.org/abs/2507.14311 https://

Leveraging Covariates in Regression Discontinuity Designs
It is common practice to incorporate additional covariates in empirical economics. In the context of Regression Discontinuity (RD) designs, covariate adjustment plays multiple roles, making it essential to understand its impact on analysis and conclusions. Typically implemented via local least squares regressions, covariate adjustment can serve three main distinct purposes: (i) improving the efficiency of RD average causal effect estimators, (ii) learning about heterogeneous RD policy effects, …

Counterfactual Survival Q Learning for Longitudinal Randomized Trials via Buckley James Boosting
Jeongjin Lee, Jong-Min Kim
https://arxiv.org/abs/2508.11060 https://

Counterfactual Survival Q Learning for Longitudinal Randomized Trials via Buckley James Boosting
We propose a Buckley James (BJ) Boost Q learning framework for estimating optimal dynamic treatment regimes under right censored survival data, tailored for longitudinal randomized clinical trial settings. The method integrates accelerated failure time models with iterative boosting techniques, including componentwise least squares and regression trees, within a counterfactual Q learning framework. By directly modeling conditional survival time, BJ Boost Q learning avoids the restrictive propor…