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This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

Statistics Theory · Mathematics 2014-02-14 Anders Bredahl Kock

For high dimensional sparse linear regression problems, we propose a sequential convex relaxation algorithm (iSCRA-TL1) by solving inexactly a sequence of truncated $\ell_1$-norm regularized minimization problems, in which the working index…

Statistics Theory · Mathematics 2024-11-05 Shujun Bi , Yonghua Yang , Shaohua Pan

In this paper, we develop a restricted eigenvalue condition for unit-root non-stationary data and derive its validity under the assumption of independent Gaussian innovations that may be contemporaneously correlated. The method of proof…

Econometrics · Economics 2022-08-30 Etienne Wijler

We consider the most common variants of linear regression, including Ridge, Lasso and Support-vector regression, in a setting where the learner is allowed to observe only a fixed number of attributes of each example at training time. We…

Machine Learning · Computer Science 2012-06-22 Elad Hazan , Tomer Koren

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

Machine Learning · Statistics 2022-05-17 Hsin-Hsiung Huang , Feng Yu , Xing Fan , Teng Zhang

This paper investigates the statistical estimation of a discrete mixing measure $\mu$0 involved in a kernel mixture model. Using some recent advances in l1-regularization over the space of measures, we introduce a "data fitting and…

Statistics Theory · Mathematics 2020-06-22 Yohann de Castro , Sébastien Gadat , Clément Marteau , Cathy Maugis

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…

Statistics Theory · Mathematics 2017-08-03 Jianqing Fan , Runlong Tang , Xiaofeng Shi

In this paper, we discuss the statistical properties of the $\ell_q$ optimization methods $(0<q\leq 1)$, including the $\ell_q$ minimization method and the $\ell_q$ regularization method, for estimating a sparse parameter from noisy…

Machine Learning · Statistics 2019-11-14 Xin Li , Yaohua Hu , Chong Li , Xiaoqi Yang , Tianzi Jiang

Sparse autoencoders (SAEs) are widely used in mechanistic interpretability to project LLM activations onto sparse latent spaces. However, sparsity alone is an imperfect proxy for interpretability, and current training objectives often…

Machine Learning · Computer Science 2026-04-09 Vivek Narayanaswamy , Kowshik Thopalli , Bhavya Kailkhura , Wesam Sakla

Choosing between classical and Bayesian sparse regression methods involves a real trade-off: penalized estimators like Lasso run in milliseconds but give no uncertainty estimates,while Horseshoe and Spike-and-Slab priors produce full…

Machine Learning · Computer Science 2026-05-05 Hao Xiao

The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed…

Statistics Theory · Mathematics 2013-07-03 Gabriela Ciuperca

Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…

Machine Learning · Computer Science 2019-07-09 Frank Nussbaum , Joachim Giesen

Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that…

Information Theory · Computer Science 2016-02-08 Mikko Vehkapera , Yoshiyuki Kabashima , Saikat Chatterjee

Many theoretical results for the lasso require the samples to be iid. Recent work has provided guarantees for the lasso assuming that the time series is generated by a sparse Vector Auto-Regressive (VAR) model with Gaussian innovations.…

Statistics Theory · Mathematics 2019-03-22 Kam Chung Wong , Zifan Li , Ambuj Tewari

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we…

Statistics Theory · Mathematics 2019-07-31 Jelena Bradic , Jianqing Fan , Jiancheng Jiang

Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…

Machine Learning · Statistics 2018-02-23 Masaaki Takada , Taiji Suzuki , Hironori Fujisawa

The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for discrete multivariate time series.…

Methodology · Statistics 2025-03-07 Trevor D. Ruiz , Sharmodeep Bhattacharyya , Sarah C. Emerson

High-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known.But when observations are scarce or corrupted, the learning task becomes much harder.The question is:…

Signal Processing · Electrical Eng. & Systems 2022-05-06 Guillaume Dalle , Yohann de Castro

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with…

Statistics Theory · Mathematics 2015-03-20 Jianqing Fan , Yingying Fan , Emre Barut

In this article, we study the asymptotic behaviour of the residual autocorrelations for periodic vector autoregressive time series models (PVAR henceforth) with uncorrelated but dependent innovations (i.e., weak PVAR). We then deduce the…

Statistics Theory · Mathematics 2024-10-01 Yacouba Boubacar Mainassara , Eugen Ursu