arXiv:2602. 16568v2 Announce Type: replace-cross Abstract: Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics.
arXiv:2606. 14335v1 Announce Type: cross Abstract: Recovering structural information from noisy high-dimensional data is a fundamental task in statistical inference.
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.
The paper investigates restricted eigenvalue (RE) bounds for norm‑regularized estimators under heavy‑tailed designs. It shows that the previously conjectured sample‑size law based on Gaussian width fails for heavy‑tailed measurements, due to a phenomenon called simultaneous threshold occupancy. The authors provide explicit counterexamples, derive worst‑case sample‑complexity bounds, and compare the behavior of heavy‑tailed versus Gaussian designs on constant‑width polyhedral descent cones.
The paper investigates how to distinguish and recover a sparse rank‑one signal in a spiked Wigner model where both the signal and the noise are independently sparse. It introduces a leave‑one‑out quadratic thresholding method that identifies the signal support for sub‑Gaussian noise and bounded spikes, and shows that sign synchronization and spectral refinement can achieve exact or strong recovery for Rademacher spikes. The work also extends to sub‑Gaussian spike priors, provides an explicit trade‑off between signal sparsity, noise sparsity, and computational cost, and establishes recoverability conditions that do not rely on moment assumptions for continuous noise.
arXiv:2609.06182v1 Announce Type: cross Abstract: In this paper, we develop and analyze techniques for recovering a linear image $Bx$ of an unknown signal $x$ from indirect noisy observation $\omega=...
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,...
arXiv:2603. 13826v2 Announce Type: replace Abstract: Classical sparse recovery treats all nonzero entries equally, though numerical noise often creates long tails of negligible coefficients.
arXiv:2609.08873v1 Announce Type: cross Abstract: Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over th...
The paper develops a mathematical theory of superposition in neural networks using frame theory and compressed sensing. It shows that a sparse binary vector of active features can be encoded by an overcomplete dictionary and recovered via a ReLU operation with a suitable bias. The authors prove recovery theorems for both random-support and worst-case support settings, providing high-probability guarantees for low-coherence dictionaries and a sharp criterion for sparsity levels, with explicit results for Gaussian random matrices and equiangular tight frames.
arXiv:2607. 14304v1 Announce Type: cross Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold.
arXiv:2609.20520v2 Announce Type: replace-cross Abstract: We prove sharp spectral-norm bounds and construct a mean-fitting regularization procedure for sparse random tensors of fixed order $k$. For a...