Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.30622

Sharp convergence rate of the estimation error of LASSO via the Feature Space Decomposition method

Guillaume Lecué·Zong Shang
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we use the Feature Space Decomposition (FSD) method to establish an explicit, non-asymptotic, instance-optimal convergence rate for the estimation error of the LASSO in the Gaussian linear regression problem for any signal, any diagonal covariance and any regularization parameter above $σ_ξ/\sqrt{N}$ where $σ_ξ$ is the noise variance and $N$ the number of data.

Explore related subjects

math.STstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Guillaume Lecué, Zong Shang. 2026-10-22. Sharp convergence rate of the estimation error of LASSO via the Feature Space Decomposition method. https://arxiv.org/abs/2610.30622

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Optimal Clustering of Multi-layer Networks under Mixture Block Models

We study clustering for multi-layer networks, where each observation is an undirected network measured on the same set of vertices. Under the mixture multi-layer stochastic block model (MMSBM), each network is generated from one of two stochastic block models, and the goal is to recover the latent network labels. We establish the minimax optimal network clustering error rate, which takes an exponential form and is characterized by the Chernoff information between the edge probability distributions of the component networks. We propose a novel two-stage estimator that combines tensor-based initialization, node and sample splitting, and a likelihood-based refinement. The refinement step exploits estimated node communities and achieves the minimax rate with high probability under extreme network sparsity. We further extend the likelihood-refinement framework to count-weighted networks through a mixture multi-layer Poisson block model. Numerical studies and two real-data analyses illustrate the finite-sample behavior of the proposed method and its use for both external-label benchmarking and unlabeled exploratory network clustering.

math.ST↗
arXiv2026

Multiply Robust Conformal Risk Control with Coarsened Data

Conformal Prediction (CP) provides prediction sets with formal coverage guarantees, but most existing methods assume fully observed training and calibration data. In many applications, however, outcomes, covariates, or both may be missing or coarsened. We develop a general framework for predictive inference with coarsened data by combining semiparametric theory with conformal methods. We introduce two complementary procedures. $(i)$ Robust Split Prediction (RSP) generalizes the doubly robust estimating-equation approach of Yang et al. [2024] beyond the classical missing outcome problem by constructing an efficient influence function based estimating equation and solving its empirical analogue. This yields multiply robust prediction sets under general coarsening patterns. $(ii)$ Robust Split Conformal Prediction (RSCP) instead combines semiparametric theory with conformal risk control. Because efficient influence functions are generally non-monotone in the threshold, we first estimate the target threshold on an independent sample and freeze the threshold-dependent nuisance functions at this preliminary estimate. This restores monotonicity and allows standard conformal risk control arguments to be applied. The resulting coverage guarantees inherit the higher-order mixed-bias structure of the influence function. We develop the theory for classical, multi-stage monotone, and non-monotone missingness and illustrate the performance of the methods through simulations and a longitudinal rheumatoid-arthritis application.

math.ST↗
arXiv2026

Exact Sign Recovery for PCA Connectivity Analysis in Mixture Models

We study exact sign recovery for PCA connectivity analysis in mixture models, using the projection onto the first $(K-1)$ principal components. For any fixed number of components with affinely independent means, we derive the oracle signal projection explicitly. Under anisotropic sub-Gaussian noise, with a random number of observations in each component, a rowwise eigenspace bound yields a sufficient condition, governed by the weakest signal direction, for recovering all connectivity signs without requiring a bounded condition number of the nonzero signal spectrum. Under isotropic Gaussian noise, when the configuration of the component means is fixed up to scaling and orthogonal transformations, we identify an asymptotically sharp threshold for the signal strength: exact sign recovery succeeds above the threshold and fails below the threshold, with probability tending to one when the signal strength stays a fixed relative distance from the threshold. The threshold has an explicit formula when the mixing proportions are equal and the means form a regular simplex.

math.ST↗