arXiv:2610.35428v1 Announce Type: new Abstract: Structured sparse learning is a leading paradigm for high-dimensional data modeling, as it enables rigorous integration of domain-validated structural...
The paper presents high‑probability generalization guarantees for Randomized Block Coordinate Descent (RBCD) when applied to nonconvex learning problems. It derives bounds on the gradients of both empirical and population risks under standard smoothness assumptions, and shows how polynomially decaying step sizes and early stopping can achieve optimal convergence rates for population gradients. In settings where the objective is gradient‑dominated, the authors provide functional suboptimality bounds that approach optimistic rates seen in convex or low‑noise scenarios, and they also establish dimension‑independent bounds for loss functions with a particular structure, extending applicability to high‑dimensional problems.
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...
arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.
arXiv:2606. 15832v1 Announce Type: new Abstract: Empirical risk minimization on massive datasets naturally exhibits a nested double finite-sum structure, where $N=nm$ total samples are logically or physically partitioned into $n$ blocks of size $m$ (e.
The paper develops a rigorous framework for computing the Normalized Maximum Likelihood (NML) codelength for regular path‑differentiable Lipschitz (PDL) estimators, which include non‑smooth models such as Lasso and Sparse SVMs. By leveraging geometric measure theory and a novel Propose‑and‑Project Metropolis‑Hastings sampler, the authors provide a method to exactly evaluate the stochastic complexity for these non‑smooth estimators and demonstrate its scalability to high‑dimensional settings. The study shows that the exact NML criterion can match cross‑validation performance while being more data‑efficient, offering a theoretically grounded alternative for model selection in modern machine learning.
arXiv:2607. 00275v1 Announce Type: cross Abstract: Federated Learning (FL) is a distributed machine learning (ML) paradigm with collaboration among multiple clients without sharing data.
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:2606. 01521v1 Announce Type: new Abstract: A central problem in machine learning is that models can achieve near-perfect training performance while generalizing substantially less well to unseen examples.
arXiv:2610. 27502v1 Announce Type: cross Abstract: Approximate leave-one-out (ALO) refers to methods that provide computationally efficient and statistically accurate approximations to leave-one-out risk estimation.
We study machine unlearning: the removal of memorized training data from a trained model. Specifically, we investigate the algorithmic complexity of certified unlearning from an optimization perspective.
arXiv:2607. 20192v1 Announce Type: new Abstract: We study machine unlearning: the removal of memorized training data from a trained model.