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We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…

Statistics Theory · Mathematics 2024-05-24 Kazuma Sawaya , Yoshimasa Uematsu , Masaaki Imaizumi

Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit…

Machine Learning · Statistics 2024-02-15 Eliot Wong-Toi , Alex Boyd , Vincent Fortuin , Stephan Mandt

We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is…

Machine Learning · Statistics 2025-08-06 Takashi Takahashi , Yoshiyuki Kabashima

Meta-learning has arisen as a successful method for improving training performance by training over many similar tasks, especially with deep neural networks (DNNs). However, the theoretical understanding of when and why overparameterized…

Machine Learning · Computer Science 2023-04-11 Peizhong Ju , Yingbin Liang , Ness B. Shroff

High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…

Methodology · Statistics 2026-02-25 Xiaoning Kang , Lulu Kang

We investigate the high-dimensional linear regression problem in the presence of noise correlated with Gaussian covariates. This correlation, known as endogeneity in regression models, often arises from unobserved variables and other…

Statistics Theory · Mathematics 2023-10-23 Toshiki Tsuda , Masaaki Imaizumi

Pretrained vision-language models (VLMs) such as CLIP have shown impressive generalization capability in downstream vision tasks with appropriate text prompts. Instead of designing prompts manually, Context Optimization (CoOp) has been…

Computer Vision and Pattern Recognition · Computer Science 2023-02-15 Chengcheng Ma , Yang Liu , Jiankang Deng , Lingxi Xie , Weiming Dong , Changsheng Xu

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

Machine Learning · Statistics 2024-10-29 Hanwen Huang , Peng Zeng

We consider a model for logistic regression where only a subset of features of size $p$ is used for training a linear classifier over $n$ training samples. The classifier is obtained by running gradient descent (GD) on logistic loss. For…

Machine Learning · Statistics 2020-05-12 Zeyu Deng , Abla Kammoun , Christos Thrampoulidis

Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…

Methodology · Statistics 2022-08-19 Qian Zhao , Emmanuel J. Candes

A major component of overfitting in model-free reinforcement learning (RL) involves the case where the agent may mistakenly correlate reward with certain spurious features from the observations generated by the Markov Decision Process…

Machine Learning · Computer Science 2020-01-01 Xingyou Song , Yiding Jiang , Stephen Tu , Yilun Du , Behnam Neyshabur

Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…

Methodology · Statistics 2026-05-01 Jing Ouyang , Chengyu Cui , Yunxiao Chen , Kean Ming Tan , Gongjun Xu

We demonstrate the first algorithms for the problem of regression for generalized linear models (GLMs) in the presence of additive oblivious noise. We assume we have sample access to examples $(x, y)$ where $y$ is a noisy measurement of…

Data Structures and Algorithms · Computer Science 2023-09-29 Ilias Diakonikolas , Sushrut Karmalkar , Jongho Park , Christos Tzamos

We study the asymptotic behaviour of the Regularized Maximum Partial Likelihood Estimator (RMPLE) in the proportional limit, considering an arbitrary convex regularizer and assuming that the covariates $\mathbf{X}_i\in\mathbb{R}^{p}$ follow…

Statistics Theory · Mathematics 2025-02-07 Emanuele Massa , Anthony Coolen

Leveraging the models' outputs, specifically the logits, is a common approach to estimating the test accuracy of a pre-trained neural network on out-of-distribution (OOD) samples without requiring access to the corresponding ground truth…

Machine Learning · Computer Science 2024-11-26 Renchunzi Xie , Ambroise Odonnat , Vasilii Feofanov , Weijian Deng , Jianfeng Zhang , Bo An

Overfitting is a phenomenon that occurs when a machine learning model is trained for too long and focused too much on the exact fitness of the training samples to the provided training labels and cannot keep track of the predictive rules…

Machine Learning · Computer Science 2025-09-22 Nuri Korhan , Samet Bayram

The large scale structure (LSS) of the universe is generated by the linear density gaussian modes, which are evolved into the observed nonlinear LSS. The posterior surface of the modes is convex in the linear regime, leading to a unique…

Cosmology and Nongalactic Astrophysics · Physics 2018-08-08 Yu Feng , Uros Seljak , Matias Zaldarriaga

One of the major open problems in machine learning is to characterize generalization in the overparameterized regime, where most traditional generalization bounds become inconsistent even for overparameterized linear regression. In many…

Machine Learning · Computer Science 2023-11-22 Jing Xu , Jiaye Teng , Yang Yuan , Andrew Chi-Chih Yao

Generalized linear models (GLMs) are popular for data-analysis in almost all quantitative sciences, but the choice of likelihood family and link function is often difficult. This motivates the search for likelihoods and links that minimize…

Methodology · Statistics 2024-03-19 Maximilian Scholz , Paul-Christian Bürkner

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

Methodology · Statistics 2026-03-03 Linglingzhi Zhu , Jonghyeok Lee , Yao Xie