The paper proposes a unified framework for estimating sparse precision and covariance matrices by reparametrizing the last column of either matrix. This reparametrization reduces the likelihood optimization to a one‑dimensional minimization followed by a penalized multiple regression, applicable to any penalty separable in off‑diagonal entries and linear on the diagonal. When the penalty is the α1 norm, the method simultaneously recovers the graphical Lasso and the covariance graphical Lasso algorithms.
arXiv:2607. 07735v1 Announce Type: cross Abstract: Sparse precision matrix estimation provides an interpretable and computationally efficient framework for modeling conditional dependencies in high-dimensional, low-sample-size data.
arXiv:2306. 14851v5 Announce Type: replace-cross Abstract: Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner.
The paper introduces a two‑stage method for estimating sparse high‑dimensional partial correlation matrices and inverse covariance matrices with non‑asymptotic guarantees. It leverages the link between inverse covariance and linear regression while ensuring positive semi‑definiteness, and provides an efficient proximal splitting algorithm for computation. The authors demonstrate the method’s effectiveness on synthetic and real‑world datasets.
arXiv:2610.33957v1 Announce Type: cross Abstract: We propose a joint sparse sample weighting and parameter estimation (SWAPE) framework that jointly optimizes model parameters and sample weights to t...
The paper introduces an online generalized-sparsity-constrained regression framework that addresses key challenges in online sparse regression, such as dynamic regularization, memory usage, and real-time computation. It proposes an efficient online hard‑thresholding algorithm that performs closed‑form updates using only summary statistics, achieving global convergence at optimal statistical rates when the projection set is overparameterized. Numerical experiments show the method consistently outperforms existing alternatives in online cardinality‑constrained linear regression and low‑rank matrix sensing.
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.
arXiv:2410. 01669v3 Announce Type: replace Abstract: Covariance Neural Networks (VNNs) perform graph convolutions on the covariance matrix of input data to leverage correlation information as pairwise connections.
arXiv:1907.06994v2 Announce Type: replace-cross Abstract: Mixtures of experts (MoE) are conditional mixture models in which both the mixing proportions and the component densities depend on the predi...
arXiv:2606. 03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data.
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...
arXiv:2606. 11738v1 Announce Type: cross Abstract: We study online estimation for high-dimensional generalized linear models with streaming data.
arXiv:2610.27010v1 Announce Type: cross Abstract: We study robust estimation of a Gaussian precision matrix that decomposes as a sparse matrix minus a symmetric, possibly indefinite, low-rank matrix,...