Tootfinder

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…

Estimation in linear models with clustered data
Anna Mikusheva, Mikkel S{\o}lvsten, Baiyun Jing
https://arxiv.org/abs/2508.12860 https://arxiv.org/pdf/2508…

Estimation in linear models with clustered data
We study linear regression models with clustered data, high-dimensional controls, and a complicated structure of exclusion restrictions. We propose a correctly centered internal IV estimator that accommodates a variety of exclusion restrictions and permits within-cluster dependence. The estimator has a simple leave-out interpretation and remains computationally tractable. We derive a central limit theorem for its quadratic form and propose a robust variance estimator. We also develop inference …

On the Rate of Gaussian Approximation for Linear Regression Problems
Marat Khusainov, Marina Sheshukova, Alain Durmus, Sergey Samsonov
https://arxiv.org/abs/2509.14039 https://

On the Rate of Gaussian Approximation for Linear Regression Problems
In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate upon the problem dimension $d$ and quantities related to the design matrix. When the number of iterations $n$ is known in advance, our results yield the rate of normal approximation of order $\sqrt{\log{n}/n}$, provided that the sample size $n$ is large enoug…

Data coarse graining can improve model performance
Alex Nguyen, David J. Schwab, Vudtiwat Ngampruetikorn
https://arxiv.org/abs/2509.14498 https://arxiv.org…

Data coarse graining can improve model performance
Lossy data transformations by definition lose information. Yet, in modern machine learning, methods like data pruning and lossy data augmentation can help improve generalization performance. We study this paradox using a solvable model of high-dimensional, ridge-regularized linear regression under 'data coarse graining.' Inspired by the renormalization group in statistical physics, we analyze coarse-graining schemes that systematically discard features based on their relevance to the learning t…

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure
Micha{\l} Derezi\'nski, Aaron Sidford
https://arxiv.org/abs/2507.11724 …

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms succeed whp. and run in time $\tilde O(d^2 + k^ω)$. For solving such regression problems in a matrix $\mathbf{A} \in \mathbb{R}^{n \times d}$ our methods succeed whp. and run in time $\tilde O(\mathrm{nnz}(\mathbf{A}) + d^2 + k^ω)$ where $ω$ is the matrix mult…

Fast and Efficient Implementation of the Maximum Likelihood Estimation for the Linear Regression with Gaussian Model Uncertainty
Ruohai Guo, Jiang Zhu, Xing Jiang, Fengzhong Qu
https://arxiv.org/abs/2507.11249

Fast and Efficient Implementation of the Maximum Likelihood Estimation for the Linear Regression with Gaussian Model Uncertainty
The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood estimation (MLE) problem was established, and the corresponding Cramer-Rao bound (CRB) was derived, leading to the development of an efficient bisection-based algorithm known as RV-ML. In contrast, this work extends the analysis to both overdetermined and underde…

KOO Method-based Consistent Clustering for Group-wise Linear Regression with Graph Structure
M. Ohishi, R. Oda
https://arxiv.org/abs/2509.11103 https://arx…

KOO Method-based Consistent Clustering for Group-wise Linear Regression with Graph Structure
The kick-one-out (KOO) method is a variable selection method based on a model selection criterion. The method is very simple, and yet it has consistency in variable selection under a high-dimensional asymptotic framework with a specific model selection criterion. This paper proposes the join-twotogether (JTT) method, which is a clustering method based on the KOO method for group-wise linear regression with graph structure. The JTT method formulates the clustering problem as an edge selection pr…

Robust Non-Linear Correlations via Polynomial Regression
Luca Giuliani, Michele Lombardi
https://arxiv.org/abs/2509.09380 https://arxiv.org/pdf/2509.09380

Robust Non-Linear Correlations via Polynomial Regression
The Hirschfeld-Gebelein-Rényi (HGR) correlation coefficient is an extension of Pearson's correlation that is not limited to linear correlations, with potential applications in algorithmic fairness, scientific analysis, and causal discovery. Recently, novel algorithms to estimate HGR in a differentiable manner have been proposed to facilitate its use as a loss regularizer in constrained machine learning applications. However, the inherent uncomputability of HGR requires a bias-variance trade-of…

A Type 2 Fuzzy Set Approach for Building Linear Linguistic Regression Analysis under Multi Uncertainty
Junzo Watada, Pei-Chun Lin, Bo Wang, Jeng-Shyang Pan, Jose Guadalupe Flores Muniz
https://arxiv.org/abs/2509.10498

A Type 2 Fuzzy Set Approach for Building Linear Linguistic Regression Analysis under Multi Uncertainty
In this paper, we propose a novel heuristic algorithm for constructing a Type-2 Fuzzy Set of the Linear Linguistic Regression (T2F-LLR) model, designed to address uncertainty and vagueness in real-world decision-making. We consider a practical scenario involving a cosmetic company's promotional planning across four product categories: Basic Face Care, Face Cleaning, Cosmetics, and Body Care, aimed at both male and female consumers. Data are collected using fuzzy linguistic questionnaires from c…

To What Extent Can Public Equity Indices Statistically Hedge Real Purchasing Power Loss in Compounded Structural Emerging-Market Crises? An Explainable ML-Based Assessment
Artem Alkhamov, Boris Kriuk
https://arxiv.org/abs/2507.13055

To What Extent Can Public Equity Indices Statistically Hedge Real Purchasing Power Loss in Compounded Structural Emerging-Market Crises? An Explainable ML-Based Assessment
This study investigates the extent to which local public equity indices can statistically hedge real purchasing power loss during compounded structural macro-financial collapses in emerging markets. We employ a non-linear multiplicative real return calculations consistent with Fisher-parity logics for both domestic and foreign investors with a principled quantile regression, tail dependence copula analysis, and Shapley Additive Explanations (SHAP) to assess the explanatory power of macro variab…

Bayesian Double Machine Learning for Causal Inference
Francis J. DiTraglia, Laura Liu
https://arxiv.org/abs/2508.12688 https://arxiv.org/pdf/2508.12688

Bayesian Double Machine Learning for Causal Inference
This paper proposes a simple, novel, and fully-Bayesian approach for causal inference in partially linear models with high-dimensional control variables. Off-the-shelf machine learning methods can introduce biases in the causal parameter known as regularization-induced confounding. To address this, we propose a Bayesian Double Machine Learning (BDML) method, which modifies a standard Bayesian multivariate regression model and recovers the causal effect of interest from the reduced-form covarian…

Approximating Euler Totient Function using Linear Regression on RSA moduli
Gilda Rech Bansimba, Regis F. Babindamana, Beni Blaug N. Ibara
https://arxiv.org/abs/2507.06706

Approximating Euler Totient Function using Linear Regression on RSA moduli
The security of the RSA cryptosystem is based on the intractability of computing Euler's totient function phi(n) for large integers n. Although deriving phi(n) deterministically remains computationally infeasible for cryptographically relevant bit lengths, and machine learning presents a promising alternative for constructing efficient approximations. In this work, we explore a machine learning approach to approximate Euler's totient function phi using linear regression models. We consider a da…

Vulnerability Patching Across Software Products and Software Components: A Case Study of Red Hat's Product Portfolio
Jukka Ruohonen, Sani Abdullahi, Abhishek Tiwari
https://arxiv.org/abs/2509.13117

Vulnerability Patching Across Software Products and Software Components: A Case Study of Red Hat's Product Portfolio
Motivated by software maintenance and the more recent concept of security debt, the paper presents a time series analysis of vulnerability patching of Red Hat's products and components between 1999 and 2024. According to the results based on segmented regression analysis, the amounts of vulnerable products and components have not been stable; a linear trend describes many of the series well. Nor do the amounts align well with trends characterizing vulnerabilities in general. There are also visi…

Stealing Accuracy: Predicting Day-ahead Electricity Prices with Temporal Hierarchy Forecasting (THieF)
Arkadiusz Lipiecki, Kaja Bilinska, Nicolaos Kourentzes, Rafal Weron
https://arxiv.org/abs/2508.11372

Stealing Accuracy: Predicting Day-ahead Electricity Prices with Temporal Hierarchy Forecasting (THieF)
We introduce the concept of temporal hierarchy forecasting (THieF) in predicting day-ahead electricity prices and show that reconciling forecasts for hourly products, 2- to 12-hour blocks, and baseload contracts significantly (up to 13%) improves accuracy at all levels. These results remain consistent throughout a challenging 4-year test period (2021-2024) in the German power market and across model architectures, including linear regression, a shallow neural network, gradient boosting, and a s…

Algorithm Design and Comparative Test of Natural Gradient Gaussian Approximation Filter
Wenhan Cao, Tianyi Zhang, Shengbo Eben Li
https://arxiv.org/abs/2507.11872

Algorithm Design and Comparative Test of Natural Gradient Gaussian Approximation Filter
Popular Bayes filters typically rely on linearization techniques such as Taylor series expansion and stochastic linear regression to use the structure of standard Kalman filter. These techniques may introduce large estimation errors in nonlinear and non-Gaussian systems. This paper overviews a recent breakthrough in filtering algorithm design called \textit{N}atural Gr\textit{a}dient Gaussia\textit{n} Appr\textit{o}ximation (NANO) filter and compare its performance over a large class of nonline…

Assisting the Grading of a Handwritten General Chemistry Exam with Artificial Intelligence
Jan Cvengros, Gerd Kortemeyer
https://arxiv.org/abs/2509.10591 https://

Assisting the Grading of a Handwritten General Chemistry Exam with Artificial Intelligence
We explore the effectiveness and reliability of an artificial intelligence (AI)-based grading system for a handwritten general chemistry exam, comparing AI-assigned scores to human grading across various types of questions. Exam pages and grading rubrics were uploaded as images to account for chemical reaction equations, short and long open-ended answers, numerical and symbolic answer derivations, drawing, and sketching in pencil-and-paper format. Using linear regression analyses and psychometr…

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…

Projection-based multifidelity linear regression for data-scarce applications
Vignesh Sella, Julie Pham, Karen Willcox, Anirban Chaudhuri
https://arxiv.org/abs/2508.08517 https:…

Projection-based multifidelity linear regression for data-scarce applications
Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear regression targeting data-limited applications with high-dimensional outputs. Multifidelity methods integrate many inexpensive low-fidelity model evaluations with limited, costly high-fidelity evaluations. We introduce two projection-based multifidelity linear reg…

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…

Strong Consistency of the SIMEX Estimator in Linear Regression with a Conditionally Poisson Covariate
Aijun Yanga, Mary Lesperance, Farouk S. Nathoo
https://arxiv.org/abs/2509.04709

Strong Consistency of the SIMEX Estimator in Linear Regression with a Conditionally Poisson Covariate
This paper considers estimation for linear regression analysis with covariate measurement error arising from Poisson surrogates. We consider cases where covariates follow a conditional Poisson distribution, capturing non-Gaussian and heteroscedastic error structures. To address this, we extend the simulation extrapolation (SIMEX) algorithm to the conditional Poisson setting (POI-SIMEX), enabling robust adjustment in the absence of internal validation data. Theoretical analysis establishes stron…

Inductance Estimation for High-Power Multilayer Rectangle Planar Windings
Theofilos Papadopoulos, Antonios Antonopoulos
https://arxiv.org/abs/2507.12082 ht…

Inductance Estimation for High-Power Multilayer Rectangle Planar Windings
This paper proposes a simple and accurate monomial-like equation for estimating the inductance of Multilayer Rectangle-shaped Planar Windings (MLRPWs) for high-frequency, high-power applications. The equation consists of the power product of the geometrical dimensions, raised at individual power coefficients. The coefficients are generated via Multiple Linear Regression (MLR), based on a large set of approximately 6,000 simulated windings, with an 80/20 training/evaluation sample ratio. The res…

Nuclear Mass Predictions Using a Neural Network with Additive Gaussian Process Regression-Optimized Activation Functions
H. X. Liu, S. Manzhos, X. H. Wu
https://arxiv.org/abs/2509.08314

Nuclear Mass Predictions Using a Neural Network with Additive Gaussian Process Regression-Optimized Activation Functions
Nuclear masses are machine-learned as a function of proton and neutron numbers. The neural network with additive Gaussian process regression-optimized activation functions (GPR-NN) method is employed for the first time for this purpose. GPR-NN combines the advantages of both neural networks and Gaussian process regression, in that it possesses the expressive power of an NN, in principle allowing modeling any kind of dependence of nuclear mass on the features, and robustness of a linear regr…

Regression for spherical responses with linear and spherical covariates using a scaled link function
Shogo Kato, Kassel L. Hingee, Janice L. Scealy, Andrew T. A. Wood
https://arxiv.org/abs/2509.06204

Regression for spherical responses with linear and spherical covariates using a scaled link function
We propose a regression model in which the responses are spherical variables and the covariates include linear and/or spherical variables. A novel link function is introduced by extending the Möbius transformation on the sphere. This link function is an anisotropic mapping that enables scale control along each axis of the spherical covariates and for each linear covariate. It generalizes several well-known link functions for circular or linear covariates. Each parameter of the link function is…

Sparse Polynomial Regression under Anomalous Data
Roozbeh Abolpour, Mohammad Reza Hesamzadeh, Maryam Dehghani
https://arxiv.org/abs/2508.18199 https://arxi…

Sparse Polynomial Regression under Anomalous Data
This paper starts with the general form of the polynomial regression model. We reformulate the Sparse Polynomial Regression Model (SPRM) with anomalous data filtering as Mixed-Integer Linear Program (MILP). This MILP is then converted to a non-convex Quadratically Constrained Quadratic Program (QCQP). Through a proposed mapping, the derived QCQP is reformulated as a Fractional Program (FP). We theoretically show that the reformulated FP has better computational properties than the original QCQP…

Evidence for an intrinsic luminosity-decay correlation in GRB radio afterglows
S. P. R. Shilling, S. R. Oates, D. A. Kann, J. Patel, J. L. Racusin, B. Cenko, R. Gupta, M. Smith, L. Rhodes, K. R. Hinds, M. Nicholl, A. Breeveld, M. Page, M. De Pasquale, B. Gompertz
https://arxiv.org/abs/2508.07276

Evidence for an intrinsic luminosity-decay correlation in GRB radio afterglows
We present the discovery of a correlation, in a sample of 16 gamma-ray burst 8.5 GHz radio afterglows, between the intrinsic luminosity measured at 10 days in the rest frame, $L_{\mathrm{Radio,10d}}$, and the average rate of decay past this time, $α_{>10d}$. The correlation has a Spearman's rank coefficient of $-0.70 \pm 0.13$ at a significance of $>3σ$ and a linear regression fit of $α_{>10d} = -0.29^{+0.19}_{-0.28} \log \left(L_{\mathrm{Radio,10d}} \right) + 8.12^{+8.86}_{-5.88}$. This fin…

A new sparsity promoting residual transform operator for Lasso regression
Yao Xiao, Anne Gelb, Aditya Viswanathan
https://arxiv.org/abs/2506.22689 https://…

A new sparsity promoting residual transform operator for Lasso regression
Lasso regression is a widely employed approach within the $\ell_1$ regularization framework used to promote sparsity and recover piecewise smooth signals $f:[a,b) \rightarrow \mathbb{R}$ when the given observations are obtained from noisy, blurred, and/or incomplete data environments. In choosing the regularizing sparsity-promoting operator, it is assumed that the particular type of variability of the underlying signal, for example, piecewise constant or piecewise linear behavior across the ent…

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 …

Forward Variable Selection in Ultra-High Dimensional Linear Regression Using Gram-Schmidt Orthogonalization
Jialuo Chen, Zhaoxing Gao, Ruey S. Tsay
https://arxiv.org/abs/2507.04668

Forward Variable Selection in Ultra-High Dimensional Linear Regression Using Gram-Schmidt Orthogonalization
We investigate forward variable selection for ultra-high dimensional linear regression using a Gram-Schmidt orthogonalization procedure. Unlike the commonly used Forward Regression (FR) method, which computes regression residuals using an increasing number of selected features, or the Orthogonal Greedy Algorithm (OGA), which selects variables based on their marginal correlations with the residuals, our proposed Gram-Schmidt Forward Regression (GSFR) simplifies the selection process by evaluatin…

Serum 25-hydroxyvitamin D concentration is not associated with mental health among Aboriginal and Torres Strait Islander Peoples in Australia: a cross-sectional exploratory study
Belinda Neo (Curtin Medical School, Curtin University, Bentley, Western Australia, Australia), Noel Nannup (The Kids Research Institute Australia, Nedlands, Western Australia, Australia), Dale Tilbrook (Maalinup Aboriginal Gallery, Caversham, Western Australia, Australia), Carol Michie (The Kids Research Insti…

Serum 25-hydroxyvitamin D concentration is not associated with mental health among Aboriginal and Torres Strait Islander Peoples in Australia: a cross-sectional exploratory study
Objective: To investigate the association between serum 25-hydroxyvitamin D [25(OH)D] concentration and mental health, measured using the Kessler Psychological Distress Scale 5 (K5), among Aboriginal and Torres Strait Islander Peoples. Methods: We used cross-sectional data from the 2012-2013 Australian Aboriginal and Torres Strait Islander Health Survey. Multiple linear regression was used to test the association between serum 25(OH)D concentration and K5, adjusting for age, sex, education, rem…

Semi-parametric Functional Classification via Path Signatures Logistic Regression
Pengcheng Zeng, Siyuan Jiang
https://arxiv.org/abs/2507.06637 https://

Semi-parametric Functional Classification via Path Signatures Logistic Regression
We propose Path Signatures Logistic Regression (PSLR), a semi-parametric framework for classifying vector-valued functional data with scalar covariates. Classical functional logistic regression models rely on linear assumptions and fixed basis expansions, which limit flexibility and degrade performance under irregular sampling. PSLR overcomes these issues by leveraging truncated path signatures to construct a finite-dimensional, basis-free representation that captures nonlinear and cross-channe…

Incremental Seeded EM Algorithm for Clusterwise Linear Regression
Ye Chow Kuang, Melanie Ooi
https://arxiv.org/abs/2507.04629 https://

Incremental Seeded EM Algorithm for Clusterwise Linear Regression
This paper proposes Incremental Seeded Expectation Maximization, an algorithm that improves upon the traditional Expectation Maximization computational flow for clusterwise or finite mixture linear regression tasks. The proposed method shows significantly better performance, particularly in scenarios involving high-dimensional input, noisy data, or a large number of clusters. Alongside the new algorithm, this paper introduces the concepts of $\textit{Resolvability}$ and $\textit{X-predictabilit…

CLT in high-dimensional Bayesian linear regression with low SNR
Seunghyun Lee, Nabarun Deb, Sumit Mukherjee
https://arxiv.org/abs/2507.23285 https://arxiv.…

CLT in high-dimensional Bayesian linear regression with low SNR
We study central limit theorems for linear statistics in high-dimensional Bayesian linear regression with product priors. Unlike the existing literature where the focus is on posterior contraction, we work under a non-contracting regime where neither the likelihood nor the prior dominates the other. This is motivated by modern high-dimensional datasets characterized by a bounded signal-to-noise ratio. This work takes a first step towards understanding limit distributions for one-dimensional pro…

Correction of estimator bias in linear regression with categorical covariates with classification error
Alexandre Garcia Dias, Mariana Rodrigues Motta, Alexandre Hild Aono
https://arxiv.org/abs/2507.07245

Correction of estimator bias in linear regression with categorical covariates with classification error
The objective of this work is to propose an asymptotic correction method for the estimators of parameters from regression models with covariates subject to classification errors. A correction was developed based on the least squares estimators from regression with erroneous covariates, the marginal probability of the true covariates, and the conditional probability of the erroneous covariates given the true covariates. In this way, we can correct these estimators without the need to correct the…

Self-learning QMC: application to the classical Holstein-Spin-Fermion model
Shaozhi Li
https://arxiv.org/abs/2509.05876 https://arxiv.org/pdf/2509.05876

Self-learning QMC: application to the classical Holstein-Spin-Fermion model
To evaluate the effectiveness of machine learning in systems with competing interactions, we developed a self-learning quantum Monte Carlo (SLQMC) method to simulate the phase transition in the classical Holstein-spin-fermion model. In SLQMC, machine learning techniques are employed to approximate the free energy, thereby bypassing the need for exact diagonalization and significantly reducing computational cost. We assess the performance of SLQMC using both linear regression and neural network …

Replaced article(s) found for econ.EM. https://arxiv.org/list/econ.EM/new
[1/1]:
- Nonparametric Treatment Effect Identification in School Choice
Jiafeng Chen
https://arxiv.org/abs/2112.03872
- Potential weights and implicit causal designs in linear regression
Jiafeng Chen
https://arxiv.org/abs/2407.21119 https://mastoxiv.page/@arXiv_econEM_bot/112885535340833628
- Reinterpreting demand estimation
Jiafeng Chen
https://arxiv.org/abs/2503.23524 https://mastoxiv.page/@arXiv_econEM_bot/114262944644769755
- A step towards the integration of machine learning and classic model-based survey methods
Tomasz \.Z\k{a}d{\l}o, Adam Chwila
https://arxiv.org/abs/2402.07521 https://mastoxiv.page/@arXiv_statME_bot/111924442633277025
- Galerkin-ARIMA: A Two-Stage Polynomial Regression Framework for Fast Rolling One-Step-Ahead Forec...
Haojie Liu, Zihan Lin
https://arxiv.org/abs/2507.07469 https://mastoxiv.page/@arXiv_statML_bot/114833708254543213
toXiv_bot_toot

Minimax optimal transfer learning for high-dimensional additive regression
Seung Hyun Moon
https://arxiv.org/abs/2509.06308 https://arxiv.org/pdf/2509.0630…

Minimax optimal transfer learning for high-dimensional additive regression
This paper studies high-dimensional additive regression under the transfer learning framework, where one observes samples from a target population together with auxiliary samples from different but potentially related regression models. We first introduce a target-only estimation procedure based on the smooth backfitting estimator with local linear smoothing. In contrast to previous work, we establish general error bounds under sub-Weibull($α$) noise, thereby accommodating heavy-tailed error d…

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…

Evaluating Ethnic Income Gap in China: The Case of Han, Mongol, and Manchu in Liaoning and Inner Mongolia
Xinyan Deng
https://arxiv.org/abs/2508.21625 https://

Evaluating Ethnic Income Gap in China: The Case of Han, Mongol, and Manchu in Liaoning and Inner Mongolia
This study analyzes the 2018 Chinese Household Income Project survey data to evaluate the income gaps between an "outsider" ethnic minority group, the Mongols, an "insider" ethnic minority group, the Manchus, and the majority Han group in urban and rural areas of Liaoning province and Inner Mongolia in China. Three statistical methods, a simple first-order OLS linear regression, linear regressions with interaction terms, and the Blinder-Oaxaca Decomposition, are used to investigate the income d…

Semi-supervised learning for linear extremile regression
Rong Jiang, Keming Yu, Jiangfeng Wang
https://arxiv.org/abs/2507.01314 https://

Semi-supervised learning for linear extremile regression
Extremile regression, as a least squares analog of quantile regression, is potentially useful tool for modeling and understanding the extreme tails of a distribution. However, existing extremile regression methods, as nonparametric approaches, may face challenges in high-dimensional settings due to data sparsity, computational inefficiency, and the risk of overfitting. While linear regression serves as the foundation for many other statistical and machine learning models due to its simplicity, …

CPC-CMS: Cognitive Pairwise Comparison Classification Model Selection Framework for Document-level Sentiment Analysis
Jianfei Li, Kevin Kam Fung Yuen
https://arxiv.org/abs/2507.14022

CPC-CMS: Cognitive Pairwise Comparison Classification Model Selection Framework for Document-level Sentiment Analysis
This study proposes the Cognitive Pairwise Comparison Classification Model Selection (CPC-CMS) framework for document-level sentiment analysis. The CPC, based on expert knowledge judgment, is used to calculate the weights of evaluation criteria, including accuracy, precision, recall, F1-score, specificity, Matthews Correlation Coefficient (MCC), Cohen's Kappa (Kappa), and efficiency. Naive Bayes, Linear Support Vector Classification (LSVC), Random Forest, Logistic Regression, Extreme Gradient B…

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…

Identifiability in Unlinked Linear Regression: Some Results and Open Problems
Fadoua Balabdaoui, Martin Slawski, Jonathan Steffani
https://arxiv.org/abs/2507.14986

Identifiability in Unlinked Linear Regression: Some Results and Open Problems
A tacit assumption in classical linear regression problems is the full knowledge of the existing link between the covariates and responses. In Unlinked Linear Regression (ULR) this link is either partially or completely missing. While the reasons causing such missingness can be different, a common challenge in statistical inference is the potential non-identifiability of the regression parameter. In this note, we review the existing literature on identifiability when the $d \ge 2$ components of…

Bayesian Additive Regression Trees for functional ANOVA model
Seokhun Park, Insung Kong, Yongdai Kim
https://arxiv.org/abs/2509.03317 https://arxiv.org/pdf…

Bayesian Additive Regression Trees for functional ANOVA model
Bayesian Additive Regression Trees (BART) is a powerful statistical model that leverages the strengths of Bayesian inference and regression trees. It has received significant attention for capturing complex non-linear relationships and interactions among predictors. However, the accuracy of BART often comes at the cost of interpretability. To address this limitation, we propose ANOVA Bayesian Additive Regression Trees (ANOVA-BART), a novel extension of BART based on the functional ANOVA decompo…

A Regression-Based Share Market Prediction Model for Bangladesh
Syeda Tasnim Fabiha, Rubaiyat Jahan Mumu, Farzana Aktar, B M Mainul Hossain
https://arxiv.org/abs/2507.18643 http…

A Regression-Based Share Market Prediction Model for Bangladesh
Share market is one of the most important sectors of economic development of a country. Everyday almost all companies issue their shares and investors buy and sell shares of these companies. Generally investors want to buy shares of the companies whose market liquidity is comparatively greater. Market liquidity depends on the average price of a share. In this paper, a thorough linear regression analysis has been performed on the stock market data of Dhaka Stock Exchange. Later, the linear model…

On the role of the design phase in a linear regression
Junho Choi
https://arxiv.org/abs/2509.01861 https://arxiv.org/pdf/2509.01861

On the role of the design phase in a linear regression
The "design phase" refers to a stage in observational studies, during which a researcher constructs a subsample that achieves a better balance in covariate distributions between the treated and untreated units. In this paper, we study the role of this preliminary phase in the context of linear regression, offering a justification for its utility. To that end, we first formalize the design phase as a process of estimand adjustment via selecting a subsample. Then, we show that covariate balance o…

Crosslisted article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Physics-Informed Regression: Parameter Estimation in Parameter-Linear Nonlinear Dynamic Models
Nielsen, Jacobsen, Olson, S{\o}rensen, Engsig-Karup

Explainability-Driven Feature Engineering for Mid-Term Electricity Load Forecasting in ERCOT's SCENT Region
Abhiram Bhupatiraju, Sung Bum Ahn
https://arxiv.org/abs/2507.22220

Explainability-Driven Feature Engineering for Mid-Term Electricity Load Forecasting in ERCOT's SCENT Region
Accurate load forecasting is essential to the operation of modern electric power systems. Given the sensitivity of electricity demand to weather variability and temporal dynamics, capturing non-linear patterns is essential for long-term planning. This paper presents a comparative analysis of machine learning models, Linear Regression, XGBoost, LightGBM, and Long Short-Term Memory (LSTM), for forecasting system-wide electricity load up to one year in advance. Midterm forecasting has shown to be …

QUTCC: Quantile Uncertainty Training and Conformal Calibration for Imaging Inverse Problems
Cassandra Tong Ye, Shamus Li, Tyler King, Kristina Monakhova
https://arxiv.org/abs/2507.14760

QUTCC: Quantile Uncertainty Training and Conformal Calibration for Imaging Inverse Problems
Deep learning models often hallucinate, producing realistic artifacts that are not truly present in the sample. This can have dire consequences for scientific and medical inverse problems, such as MRI and microscopy denoising, where accuracy is more important than perceptual quality. Uncertainty quantification techniques, such as conformal prediction, can pinpoint outliers and provide guarantees for image regression tasks, improving reliability. However, existing methods utilize a linear consta…

High-dimensional Longitudinal Inference via a De-sparsified Dantzig-Selector
Nathan Huey, Rajarshi Mukherjee
https://arxiv.org/abs/2508.07498 https://arxiv…

High-dimensional Longitudinal Inference via a De-sparsified Dantzig-Selector
In this paper, we consider statistical inference with generalized linear models in high dimensions under a longitudinal clustered data framework. Specifically, we propose a de-sparsified version of an initial Dantzig-type regularized estimator in regression settings and provide theoretical justification for both linear and generalized linear models. We present extensive numerical simulations demonstrating the effectiveness of our method for continuous and binary data. For continuous outcomes un…

Galerkin-ARIMA: A Two-Stage Polynomial Regression Framework for Fast Rolling One-Step-Ahead Forecasting
Haojie Liu, Zihan Lin
https://arxiv.org/abs/2507.07469

Galerkin-ARIMA: A Two-Stage Polynomial Regression Framework for Fast Rolling One-Step-Ahead Forecasting
Time-series models like ARIMA remain widely used for forecasting but limited to linear assumptions and high computational cost in large and complex datasets. We propose Galerkin-ARIMA that generalizes the AR component of ARIMA and replace it with a flexible spline-based function estimated by Galerkin projection. This enables the model to capture nonlinear dependencies in lagged values and retain the MA component and Gaussian noise assumption. We derive a closed-form OLS estimator for the Galerk…

Crosslisted article(s) found for cond-mat.mtrl-sci. https://arxiv.org/list/cond-mat.mtrl-sci/new
[1/1]:
- Interpretability of linear regression models of glassy dynamics
Anand Sharma, Chen Liu, Misaki Ozawa, Daniele Coslovich

From Linear to Hierarchical: Evolving Tree-structured Thoughts for Efficient Alpha Mining
Junji Ren, Junjie Zhao, Shengcai Liu, Peng Yang
https://arxiv.org/abs/2508.16334 https:…

From Linear to Hierarchical: Evolving Tree-structured Thoughts for Efficient Alpha Mining
Alpha mining, which discovers signals that predict asset returns, has long been attractive for automatic quantitative investment. This problem is typically formulated as a tree-based symbolic regression with handcrafted market data features and arithmetic operators. Unfortunately, existing symbolic methods are concerned with computational inefficiency and dependence on prior knowledge. Recent implementation of Large Language Models (LLMs) show that they can automatically generate executable cod…

Predicting Formula 1 Race Outcomes: Decomposing the Roles of Drivers and Constructors through Linear Modeling
Saurabh Rane
https://arxiv.org/abs/2508.00200 https://

Predicting Formula 1 Race Outcomes: Decomposing the Roles of Drivers and Constructors through Linear Modeling
Formula 1 performance is a combination of the car's ability and the driver's ability. While a given race or season can tell you how well a car and driver performed jointly, isolating the individual impact of the driver and constructor remains challenging. This paper extends a Regularized Adjusted Plus Minus (RAPM) methodology (Sill 2010), commonly used in basketball and hockey, to parse out individual driver and constructor impact. It employs a time-decayed ridge regression with LOESS (Jacoby 2…

Enhanced Predictive Modeling for Hazardous Near-Earth Object Detection: A Comparative Analysis of Advanced Resampling Strategies and Machine Learning Algorithms in Planetary Risk Assessment
Sunkalp Chandra
https://arxiv.org/abs/2508.15106

Enhanced Predictive Modeling for Hazardous Near-Earth Object Detection: A Comparative Analysis of Advanced Resampling Strategies and Machine Learning Algorithms in Planetary Risk Assessment
This study evaluates the performance of several machine learning models for predicting hazardous near-Earth objects (NEOs) through a binary classification framework, including data scaling, power transformation, and cross-validation. Six classifiers were compared, namely Random Forest Classifier (RFC), Gradient Boosting Classifier (GBC), Support Vector Classifier (SVC), Linear Discriminant Analysis (LDA), Logistic Regression (LR), and K-Nearest Neighbors (KNN). RFC and GBC performed the best, b…

Analysis of Photonic Circuit Losses with Machine Learning Techniques
Adrian Nugraha Utama, Simon Chun Kiat Goh, Li Hongyu, Wang Xiangyu, Zhou Yanyan, Victor Leong, Manas Mukherjee
https://arxiv.org/abs/2506.17999

Analysis of Photonic Circuit Losses with Machine Learning Techniques
Low-loss waveguides enable efficient light delivery in photonic circuits, which are essential for high-speed optical communications and scalable implementations of photonic quantum technologies. We study the effects of several fabrication and experimental parameters on the waveguide losses of a silicon nitride integrated photonics platform using various machine learning techniques. Compared to more complex machine learning algorithms, our results show that a simple linear regression model with …

Optimal Exact Designs of Multiresponse Experiments under Linear and Sparsity Constraints
Lenka Filov\'a, P\'al Somogyi, Radoslav Harman
https://arxiv.org/abs/2507.04713

Optimal Exact Designs of Multiresponse Experiments under Linear and Sparsity Constraints
We propose a computational approach to constructing exact designs on finite design spaces that are optimal for multiresponse regression experiments under a combination of the standard linear and specific 'sparsity' constraints. The linear constraints address, for example, limits on multiple resource consumption and the problem of optimal design augmentation, while the sparsity constraints control the set of distinct trial conditions utilized by the design. The key idea is to construct an artifi…

Covariance scanning for adaptively optimal change point detection in high-dimensional linear models
Haeran Cho, Housen Li
https://arxiv.org/abs/2507.02552 …

Covariance scanning for adaptively optimal change point detection in high-dimensional linear models
This paper investigates the detection and estimation of a single change in high-dimensional linear models. We derive minimax lower bounds for the detection boundary and the estimation rate, which uncover a phase transition governed the sparsity of the covariance-weighted differential parameter. This form of "inherent sparsity" captures a delicate interplay between the covariance structure of the regressors and the change in regression coefficients on the detectability of a change point. Complem…

Empirical Models of the Time Evolution of SPX Option Prices
Alessio Brini, David A. Hsieh, Patrick Kuiper, Sean Moushegian, David Ye
https://arxiv.org/abs/2506.17511

Empirical Models of the Time Evolution of SPX Option Prices
The key objective of this paper is to develop an empirical model for pricing SPX options that can be simulated over future paths of the SPX. To accomplish this, we formulate and rigorously evaluate several statistical models, including neural network, random forest, and linear regression. These models use the observed characteristics of the options as inputs -- their price, moneyness and time-to-maturity, as well as a small set of external inputs, such as the SPX and its past history, dividend …

Bayesian Models for Joint Selection of Features and Auto-Regressive Lags: Theory and Applications in Environmental and Financial Forecasting
Alokesh Manna, Sujit K. Ghosh
https://arxiv.org/abs/2508.10055

Bayesian Models for Joint Selection of Features and Auto-Regressive Lags: Theory and Applications in Environmental and Financial Forecasting
We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on contemporaneous or past explanatory variables and persistent stochastic shocks, including financial modeling, hydrological forecasting, and meteorological applications requiring temporal dependency capture. Our methodology uses hierarchical Bayesian models w…

Derivation of Tissue Properties from Basis-Vector Model Weights for Dual-Energy CT-Based Monte Carlo Proton Beam Dose Calculations
Maria Jose Medrano, Xinyuan Chen, Lucas Norberto Burigo, Joseph A. O'Sullivan, Jeffrey F. Williamson
https://arxiv.org/abs/2506.22425

Derivation of Tissue Properties from Basis-Vector Model Weights for Dual-Energy CT-Based Monte Carlo Proton Beam Dose Calculations
We propose a novel method, basis vector model material indexing (BVM-MI), for predicting atomic composition and mass density from two independent basis vector model weights derived from dual-energy CT (DECT) for Monte Carlo (MC) dose planning. BVM-MI employs multiple linear regression on BVM weights and their quotient to predict elemental composition and mass density for 70 representative tissues. Predicted values were imported into the TOPAS MC code to simulate proton dose deposition to a unif…

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.

Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogation
Julen Cestero, Carmine Delle Femine, Kenji S. Muro, Marco Quartulli, Marcello Restelli
https://arxiv.org/abs/2508.21559

Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogation
Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in conventional data-driven methods. This paper evaluates PINNs' capabilities as surrogate models for smart grid dynamics, comparing their performance against XGBoost, Random Forest, and Linear Regression across three key experiments: interpolation, cross-validat…

Maximum-likelihood reprojections for reliable Koopman-based predictions and bifurcation analysis of parametric dynamical systems
Pieter van Goor, Robert Mahony, Manuel Schaller, Karl Worthmann
https://arxiv.org/abs/2506.17817

Maximum-likelihood reprojections for reliable Koopman-based predictions and bifurcation analysis of parametric dynamical systems
Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, data generation, learning and prediction is performed through the lens of this lifting, giving rise to a nonlinear manifold that is invariant under the Koopman operator. In data-driven approximation such as Extended Dynamic Mode Decomposition, this invariance is typically lost due to the presence of (finite-data) approximation errors. In this work, we show that reprojections are crucial for …

Adaptive Market Intelligence: A Mixture of Experts Framework for Volatility-Sensitive Stock Forecasting
Diego Vallarino
https://arxiv.org/abs/2508.02686 https://

Adaptive Market Intelligence: A Mixture of Experts Framework for Volatility-Sensitive Stock Forecasting
This study develops and empirically validates a Mixture of Experts (MoE) framework for stock price prediction across heterogeneous volatility regimes using real market data. The proposed model combines a Recurrent Neural Network (RNN) optimized for high-volatility stocks with a linear regression model tailored to stable equities. A volatility-aware gating mechanism dynamically weights the contributions of each expert based on asset classification. Using a dataset of 30 publicly traded U.S. stoc…

Generative Flexible Latent Structure Regression (GFLSR) model
Clara Grazian, Qian Jin, Pierre Lafaye De Micheaux
https://arxiv.org/abs/2508.04393 https://a…

Generative Flexible Latent Structure Regression (GFLSR) model
Latent structure methods, specifically linear continuous latent structure methods, are a type of fundamental statistical learning strategy. They are widely used for dimension reduction, regression and prediction, in the fields of chemometrics, economics, social science and etc. However, due to the lack of model inference, generative form, and unidentifiable parameters, most of these methods are always used as an algorithm, instead of a model. This paper proposed a Generative Flexible Latent Str…

Proof of The TAP Free Energy for High-Dimensional Linear Regression with Spherical Priors at All Temperatures
Zhiyuan Yu, Jingbo Liu
https://arxiv.org/abs/2506.20768

Proof of The TAP Free Energy for High-Dimensional Linear Regression with Spherical Priors at All Temperatures
Variational inference (VI) has emerged as an efficient framework for approximating intractable posteriors. Traditional mean-field VI methods fail to capture the complex dependencies and can be inconsistent in high-dimensional settings. In contrast, it has been conjectured, based on statistical physics heuristics and conditions for the stationary points, that the more refined Thouless-Anderson-Palmer (TAP) approximation is consistent in the high-dimensional regimes. Existing results, however, ha…

Nonparametric Envelopes for Flexible Response Reduction
Tate Jacobson
https://arxiv.org/abs/2509.07248 https://arxiv.org/pdf/2509.07248

Nonparametric Envelopes for Flexible Response Reduction
Envelope methods improve the estimation efficiency in multivariate linear regression by identifying and separating the material and immaterial parts of the responses or the predictors and estimating the regression coefficients using only the material part. Though envelopes have been extended to other models, such as GLMs, these extensions still largely fall under the restrictive parametric modeling framework. In this paper, we introduce a flexible, nonparametric extension of response envelopes …

Wild Bootstrap Inference for Linear Regressions with Many Covariates
Wenze Li
https://arxiv.org/abs/2506.20972 https://arxiv.org/pdf/…

Wild Bootstrap Inference for Linear Regressions with Many Covariates
We propose a simple modification to the wild bootstrap procedure and establish its asymptotic validity for linear regression models with many covariates and heteroskedastic errors. Monte Carlo simulations show that the modified wild bootstrap has excellent finite sample performance compared with alternative methods that are based on standard normal critical values, especially when the sample size is small and/or the number of controls is of the same order of magnitude as the sample size.

Learning with springs and sticks
Luis Mantilla Calder\'on, Al\'an Aspuru-Guzik
https://arxiv.org/abs/2508.19015 https://arxiv.org/pdf/2508.19015

Learning with springs and sticks
Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a piecewise-linear approximation of the given function, use the potential energy of springs to encode a desired mean squared error loss function, and converge to a minimum-energy configuration via dissipation. We apply the proposed simulation system to regression tasks …

Online design of experiments by active learning for nonlinear system identification
Kui Xie, Alberto Bemporad
https://arxiv.org/abs/2506.21754 https://

Online design of experiments by active learning for nonlinear system identification
We investigate the use of active-learning (AL) strategies to generate the input excitation signal at runtime for system identification of linear and nonlinear autoregressive and state-space models. We adapt various existing AL approaches for static model regression to the dynamic context, coupling them with a Kalman filter to update the model parameters recursively, and also cope with the presence of input and output constraints. We show the increased sample efficiency of the proposed approache…

Adaptive estimation for nonparametric circular regression with errors in variables
Tien Dat Nguyen, Thanh Mai Pham Ngoc
https://arxiv.org/abs/2508.18581 https://

Adaptive estimation for nonparametric circular regression with errors in variables
This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are constructed and their theoretical performance is assessed through convergence rates over Sobolev and Hölder smoothness classes. Numerical experiments on simulated and real datasets illustrate the practical relevance of the methodology.

Interpretable Scalar-on-Image Linear Regression Models via the Generalized Dantzig Selector
Sijia Liao, Xiaoxiao Sun, Ning Hao, Hao Helen Zhang
https://arxiv.org/abs/2508.20278 …

Interpretable Scalar-on-Image Linear Regression Models via the Generalized Dantzig Selector
The scalar-on-image regression model examines the association between a scalar response and a bivariate function (e.g., images) through the estimation of a bivariate coefficient function. Existing approaches often impose smoothness constraints to control the bias-variance trade-off, and thus prevent overfitting. However, such assumptions can hinder interpretability, especially when only certain regions of an image influence changes in the response. In such a scenario, interpretability can be be…

Scalable Bayesian inference on high-dimensional multivariate linear regression
Xuan Cao, Kyoungjae Lee
https://arxiv.org/abs/2508.16446 https://arxiv.org/p…

Scalable Bayesian inference on high-dimensional multivariate linear regression
We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous approaches that either utilize a generalized likelihood without ensuring the positive definiteness of the precision matrix or rely on maximization algorithms targeting only the posterior mode, thus failing to address uncertainty. In this work, we propose two Bayesi…

Nonparametric regression for a circular response with error-in-covariate
Nicholas Woolsey, Xianzheng Huang
https://arxiv.org/abs/2508.15962 https://arxiv.o…

Nonparametric regression for a circular response with error-in-covariate
This study considers regression analysis of a circular response with an error-prone linear covariate. Starting with an existing estimator of the circular regression function that assumes error-free covariate, three approaches are proposed to revise this estimator, leading to three nonparametric estimators for the circular regression function accounting for measurement error. The proposed estimators are intrinsically connected through some deconvoluting operator that is exploited differently in …

Dynamic Spatio-Temporal Sequential Ordinal Models: Application to Invasive Weeds
Geoffrey R. Hosack, Wen-Hsi Yang, Kyana N. Pike, Luke S. O'Loughlin, Emma Cook, Brett Howland, Emily Sutcliffe, Richard N. C. Milner, Ben Gooden, Jens G. Froese
https://arxiv.org/abs/2509.01976

Dynamic Spatio-Temporal Sequential Ordinal Models: Application to Invasive Weeds
The multivariate sequential ordinal model is investigated for use in the Bayesian analysis of spatio-temporal ordinal data. The sequential ordinal model likelihood is equivalent to a binary model conditional on unknown regression coefficients and spatio-temporal random effects. Therefore, estimation and prediction in the space-time context can proceed using the well-established dynamic generalised linear model framework. Moreover, the sequential ordinal model avoids the ordering constraints on …

Understanding Spatial Regression Models from a Weighting Perspective in an Observational Study of Superfund Remediation
Sophie M. Woodward, Francesca Dominici, Jose R. Zubizarreta
https://arxiv.org/abs/2508.19572

Understanding Spatial Regression Models from a Weighting Perspective in an Observational Study of Superfund Remediation
Superfund sites are locations in the United States with high levels of environmental toxicants, often resulting from industrial activity or improper waste management. Given mounting evidence linking prenatal environmental exposures to adverse birth outcomes, estimating the impact of Superfund remediation is of substantial policy relevance. A widespread approach is to fit a spatial regression, i.e., a linear regression of the outcome (e.g., birth weight) on binary treatment (e.g., indicator for …

A powerful transformation of quantitative responses for biobank-scale association studies
Yaowu Liu, Tianying Wang
https://arxiv.org/abs/2507.06496 https:/…

A powerful transformation of quantitative responses for biobank-scale association studies
In linear regression models with non-Gaussian errors, transformations of the response variable are widely used in a broad range of applications. Motivated by various genetic association studies, transformation methods for hypothesis testing have received substantial interest. In recent years, the rise of biobank-scale genetic studies, which feature a vast number of participants that could be around half a million, spurred the need for new transformation methods that are both powerful for detect…

General measures of effect size to calculate power and sample size for Wald tests with generalized linear models
Amy L Cochran, Shijie Yuan, Paul J Rathouz
https://arxiv.org/abs/2506.22324

General measures of effect size to calculate power and sample size for Wald tests with generalized linear models
Power and sample size calculations for Wald tests in generalized linear models (GLMs) are often limited to specific cases like logistic regression. More general methods typically require detailed study parameters that are difficult to obtain during planning. We introduce two new effect size measures for estimating power, sample size, or the minimally detectable effect size in studies using Wald tests across any GLM. These measures accommodate any number of predictors or adjusters and require on…

Bayesian Variable Selection in Multivariate Regression Under Collinearity in the Design Matrix
Joyee Ghosh, Xun Li
https://arxiv.org/abs/2507.17975 https://

Bayesian Variable Selection in Multivariate Regression Under Collinearity in the Design Matrix
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, specifying a model with a non-diagonal covariance matrix is appealing. Modeling dependency in the random errors through a non-diagonal covariance matrix is generally expected to lead to improved estimation of the regression coefficients. In this article, we highlight…

Change point detection in ERA5 ground temperature time series
Fatemeh Aghaei A., Ewan T. Phillips, Holger Kantz
https://arxiv.org/abs/2507.15045 https://…

Change point detection in ERA5 ground temperature time series
We analyze the ERA5 reanalysis 2-meter temperature time series on all land grid points using change point analysis. We fit two linear slopes to the data with the constraint that they merge at the point in time where the slope changes. We compare such fits to a standard linear regression in two ways: We use Akaike's and the Bayesian information criteria for model selection, and we test against the null hypothesis of no change of the trend value. For those grid points where the …

A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing
Joshua Agterberg, Ren\'e Vidal
https://arxiv.org/abs/2506.20659 https://

A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing
The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to this problem, establishing minimax error rates when the number of measurements is sufficiently large relative to the rank and dimension of the low-rank matrix, though a precise comparison of these procedures still remains unexplored. In this work we provide …

Regression approaches for modelling genotype-environment interaction and making predictions into unseen environments
Maksym Hrachov, Hans-Peter Piepho, Niaz Md. Farhat Rahman, Waqas Ahmed Malik
https://arxiv.org/abs/2507.18125

Regression approaches for modelling genotype-environment interaction and making predictions into unseen environments
In plant breeding and variety testing, there is an increasing interest in making use of environmental information to enhance predictions for new environments. Here, we will review linear mixed models that have been proposed for this purpose. The emphasis will be on predictions and on methods to assess the uncertainty of predictions for new environments. Our point of departure is straight-line regression, which may be extended to multiple environmental covariates and genotype-specific responses.…

The fundamental limits of minimax risk for high-dimensional speckle noise model
Hao Xing, Soham Jana, Arian Maleki
https://arxiv.org/abs/2508.18503 https://

The fundamental limits of minimax risk for high-dimensional speckle noise model
Unlike conventional imaging modalities, such as magnetic resonance imaging, which are often well described by a linear regression framework, coherent imaging systems follow a significantly more complex model. In these systems, the task is to recover the unknown signal or image $\mathbf{x}_o \in \mathbb{R}^n$ from observations $\mathbf{y}_1, \ldots, \mathbf{y}_L \in \mathbb{R}^m$ of the form \[ \mathbf{y}_l = A_l X_o \mathbf{w}_l + \mathbf{z}_l, \quad l = 1, \ldots, L, \] where $X_o = \mathrm{di…

Stochastic Taylor expansion via Poisson point processes
Weichao Wu, Athanasios C. Micheas
https://arxiv.org/abs/2508.04703 https://arxiv.org/pdf/2508.04703…

Stochastic Taylor expansion via Poisson point processes
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the model parameters. Theoretical properties of the proposed estimator are also proven, including its convergence, uniformly almost surely, to the true function. The theory is presented for the univariate and multivariate cases, and we exemplify the proposed meth…

Replaced article(s) found for math.ST. https://arxiv.org/list/math.ST/new
[1/1]:
- An extended latent factor framework for ill-posed linear regression
Gianluca Finocchio, Tatyana Krivobokova

A direct approach to tree-guided feature aggregation for high-dimensional regression
Jinwen Fu, Aaron J. Molstad, Hui Zou
https://arxiv.org/abs/2507.19650 https://

A direct approach to tree-guided feature aggregation for high-dimensional regression
In high-dimensional linear models, sparsity is often exploited to reduce variability and achieve parsimony. Equi-sparsity, where one assumes that predictors can be aggregated into groups sharing the same effects, is an alternative parsimonious structure that can be more suitable in certain applications. Previous work has clearly demonstrated the benefits of exploiting equi-sparsity in the presence of ``rare features'' (Yan and Bien 2021). In this work, we propose a new tree-guided regularizatio…

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 …

High-dimensional Asymptotics of Generalization Performance in Continual Ridge Regression
Yihan Zhao, Wenqing Su, Ying Yang
https://arxiv.org/abs/2508.15494 https://

High-dimensional Asymptotics of Generalization Performance in Continual Ridge Regression
Continual learning is motivated by the need to adapt to real-world dynamics in tasks and data distribution while mitigating catastrophic forgetting. Despite significant advances in continual learning techniques, the theoretical understanding of their generalization performance lags behind. This paper examines the theoretical properties of continual ridge regression in high-dimensional linear models, where the dimension is proportional to the sample size in each task. Using random matrix theory,…

Replaced article(s) found for stat.ME. https://arxiv.org/list/stat.ME/new
[1/1]:
- Adaptive greedy forward variable selection for linear regression models with incomplete data usin...
Yong-Shiuan Lee

FBMS: An R Package for Flexible Bayesian Model Selection and Model Averaging
Florian Frommlet, Jon Lachmann, Geir Storvik, Aliaksandr Hubin
https://arxiv.org/abs/2509.00753 http…

FBMS: An R Package for Flexible Bayesian Model Selection and Model Averaging
The FBMS R package facilitates Bayesian model selection and model averaging in complex regression settings by employing a variety of Monte Carlo model exploration methods. At its core, the package implements an efficient Mode Jumping Markov Chain Monte Carlo (MJMCMC) algorithm, designed to improve mixing in multi-modal posterior landscapes within Bayesian generalized linear models. In addition, it provides a genetically modified MJMCMC (GMJMCMC) algorithm that introduces nonlinear feature gener…

TRUST: Transparent, Robust and Ultra-Sparse Trees
Albert Dorador
https://arxiv.org/abs/2506.15791 https://arxiv.org/pdf/2506.15791

TRUST: Transparent, Robust and Ultra-Sparse Trees
Piecewise-constant regression trees remain popular for their interpretability, yet often lag behind black-box models like Random Forest in predictive accuracy. In this work, we introduce TRUST (Transparent, Robust, and Ultra-Sparse Trees), a novel regression tree model that combines the accuracy of Random Forests with the interpretability of shallow decision trees and sparse linear models. TRUST further enhances transparency by leveraging Large Language Models to generate tailored, user-friendl…

Crosslisted article(s) found for stat.ME. https://arxiv.org/list/stat.ME/new
[1/1]:
- Physics-Informed Regression: Parameter Estimation in Parameter-Linear Nonlinear Dynamic Models
Nielsen, Jacobsen, Olson, S{\o}rensen, Engsig-Karup