The paper discusses the limitations of LASSO in high‑dimensional regression models when cointegrated regressors are present, noting that the convex penalty can overly shrink their coefficients and lead to inconsistent estimation. It proposes using folded concave penalties (FCP), such as SCAD and MCP, to overcome this issue, establishing both local and global oracle properties for the penalized regression. Simulation results and an application to euro area unemployment forecasting demonstrate that FCP improves variable selection and out‑of‑sample prediction compared to LASSO.
By Hongqi Chen, Chengwang Liao, Ziwei Mei, Zhentao Shi
arXiv:2510. 11546v3 Announce Type: replace-cross Abstract: High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods.
By Meixia Lin, Mengjiao Shi, Yunhai Xiao, Qian Zhang
arXiv:2610.08345v1 Announce Type: cross
Abstract: Using a replica-symmetric high-dimensional characterization, we develop an inferential framework for sparse support vector machines when the sample s...
By Peng Zeng, Hanwen Huang
arXiv:2610. 29425v1 Announce Type: new Abstract: Understanding generalization of randomized learning algorithms remains a central challenge.
By Mohammad Hossein Momeni Hamaneh, Mohammad Mahdi Mojahedian, Mohammad Hossein Yassaee
arXiv:2607. 03839v1 Announce Type: new Abstract: Sparse feature selection is critical for high-dimensional machine learning, yet traditional $\ell_1$-regularized methods are often brittle under observational noise and spurious correlations, leading to unstable feature supports and degraded generalization.
By Zhen Huang, Peicheng Xu, Junbiao Pang, Yulong Zheng
arXiv:2606. 11738v1 Announce Type: cross Abstract: We study online estimation for high-dimensional generalized linear models with streaming data.
By Junzhuo Gao, Ling Peng, Xu Guo, Heng Lian
arXiv:2606. 06855v1 Announce Type: cross Abstract: While algorithmic stability is a central tool for understanding generalization of learning algorithms, existing high-probability guarantees typically rely on uniform boundedness or sub-Gaussian/sub-Weibull tail assumptions, which can be overly restrictive for modern settings with heavy-tailed or unbounded losses.
By Qianqian Lei, Soham Bonnerjee, Yuefeng Han, Wei Biao Wu
arXiv:2610.07721v1 Announce Type: cross
Abstract: We study ridge regression from exactly $s$ distinct rows of a fixed design. Responses are fixed, and only the subset is random. The determinant law a...
By Kihun Rhee
arXiv:2608.22597v1 Announce Type: new
Abstract: Subsampling is effective in tackling computational challenges for massive data with rare events. Overly aggressive subsampling may adversely affect est...
By Jing Wang, HaiYing Wang, Qiang Zhang, Hao Helen Zhang
The paper studies the numerical solution of the Beurling‑LASSO (BLASSO) for estimating Gaussian mixture models (GMMs) with unknown numbers of components and unknown diagonal covariance matrices. It introduces a Conic Particle Gradient Descent (CPGD) algorithm that incorporates Riemannian gradient descent to respect the Fisher‑Rao geometry of Gaussian distributions. The authors provide theoretical convergence guarantees, including exponential local convergence under a non‑degeneracy condition related to component separation, and demonstrate through numerical experiments that CPGD is more robust to overspecification of components than the EM algorithm.
By Romane Giard, Yohann De Castro, Roland Denis, Cl\'ement Marteau
We study ridge regression from exactly $s$ distinct rows of a fixed design. Responses are fixed, and only the subset is random. The determinant law and selected ridge fit share one positive definite p...
arXiv:2609.38263v1 Announce Type: new
Abstract: Feature selection in neural networks remains a challenging problem, particularly in the presence of noisy or contaminated data. LassoNet is a recent ap...
By Daniela De Canditiis, Italia De Feis, Paola Stolfi