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In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

Statistics Theory · Mathematics 2007-06-13 Ana K. Fermin , Carenne Ludena

Obtaining valid treatment effect inference remains a challenging problem when dealing with numerous instruments and non-sparse control variables. In this paper, we propose a novel ridge regularization-based instrumental variables method for…

Econometrics · Economics 2025-10-17 Xiduo Chen , Xingdong Feng , Antonio F. Galvao , Yeheng Ge

We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution. We establish general conditions that determine…

Statistics Theory · Mathematics 2024-04-02 Pratik Patil , Jin-Hong Du , Ryan J. Tibshirani

This paper establishes a precise high-dimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives. We consider a high-dimensional setting where the number of features (weak learners) $p$…

Statistics Theory · Mathematics 2022-11-21 Tengyuan Liang , Pragya Sur

We consider correlated \emph{factor} regression models (FRM) and analyze the performance of classical ridge interpolators. Utilizing powerful \emph{Random Duality Theory} (RDT) mathematical engine, we obtain \emph{precise} closed form…

Machine Learning · Statistics 2024-06-14 Mihailo Stojnic

In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…

Statistics Theory · Mathematics 2024-05-09 Piotr Zwiernik

A fundamental problem in machine learning is understanding the effect of early stopping on the parameters obtained and the generalization capabilities of the model. Even for linear models, the effect is not fully understood for arbitrary…

Machine Learning · Computer Science 2024-06-10 Rishi Sonthalia , Jackie Lok , Elizaveta Rebrova

The main theme of this paper is a modification of the likelihood ratio test (LRT) for testing high dimensional covariance matrix. Recently, the correct asymptotic distribution of the LRT for a large-dimensional case (the case $p/n$…

Methodology · Statistics 2019-04-16 Young-Geun Choi , Chi Tim Ng , Johan Lim

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily)…

Statistics Theory · Mathematics 2023-02-01 Alexis Ayme , Claire Boyer , Aymeric Dieuleveut , Erwan Scornet

Insurance pricing systems should fulfill the auto-calibration property to ensure that there is no systematic cross-financing between different price cohorts. Often, regression models are not auto-calibrated. We propose to apply isotonic…

Methodology · Statistics 2023-01-10 Mario V. Wüthrich , Johanna Ziegel

A regression model with more parameters than data points in the training data is overparametrized and has the capability to interpolate the training data. Based on the classical bias-variance tradeoff expressions, it is commonly assumed…

Machine Learning · Computer Science 2023-04-18 Tomas McKelvey

In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on…

Statistics Theory · Mathematics 2018-10-15 Mohamed Ndaoud

Separation in logistic regression is a common problem causing failure of the iterative estimation process when finding maximum likelihood estimates. Firth's correction (FC) was proposed as a solution, providing estimates also in presence of…

Methodology · Statistics 2020-12-01 Hana Šinkovec , Angelika Geroldinger , Georg Heinze , Rok Blagus

This paper aims at analyzing the regularization effect that data augmentation induces on supervised regression methods in the proportional regime, where the number of covariates grows proportionally to the number of samples. We provide a…

Machine Learning · Statistics 2026-05-12 Lucas Morisset , Alain Durmus , Adrien Hardy

This paper provides elementary analyses of the regret and generalization of minimum-norm interpolating classifiers (MNIC). The MNIC is the function of smallest Reproducing Kernel Hilbert Space norm that perfectly interpolates a label…

Machine Learning · Statistics 2021-07-30 Tengyuan Liang , Benjamin Recht

We consider penalized extremum estimation of a high-dimensional, possibly nonlinear model that is sparse in the sense that most of its parameters are zero but some are not. We use the SCAD penalty function, which provides model selection…

Econometrics · Economics 2024-02-23 Joel L. Horowitz , Ahnaf Rafi

The rule of thumb regarding the relationship between the bias-variance tradeoff and model size plays a key role in classical machine learning, but is now well-known to break down in the overparameterized setting as per the double descent…

Machine Learning · Statistics 2026-02-16 Qingyi Hu , Liam Hodgkinson

The multi-scale entanglement renormalization ansatz (MERA) provides a natural description of the ground state of a quantum critical Hamiltonian on the lattice. From an optimized MERA, one can extract the scaling dimensions of the underlying…

Strongly Correlated Electrons · Physics 2022-12-14 Javier Argüello-Luengo , Ashley Milsted , Guifre Vidal

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…

Machine Learning · Statistics 2018-10-29 Mikhail Belkin , Daniel Hsu , Partha Mitra

We study the asymptotic generalization of an overparameterized linear model for multiclass classification under the Gaussian covariates bi-level model introduced in Subramanian et al.~'22, where the number of data points, features, and…

Machine Learning · Computer Science 2025-03-28 David X. Wu , Anant Sahai