Recovering linear images of sparse signals from indirect observations
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2510. 24215v5 Announce Type: replace-cross Abstract: Recovery from linear measurements under sparse adversarial corruption is typically formulated as an exact-recovery problem: one seeks structural conditions on $\mathbf{A}$ (e.
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.
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: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 tackles learning structured linear dynamical systems when only a few observations are available at each time step. It proposes an estimator that minimizes a bias‑corrected, potentially non‑convex objective and derives non‑asymptotic error bounds that depend on the local complexity of the constraint set, the trajectory length, and the sub‑sampling probability. The authors also prove convergence of projected gradient descent and demonstrate the theory for three specific constraint sets, showing that accurate recovery of the transition matrix is achievable with much shorter trajectories and very low observation rates.
arXiv:2509.01809v2 Announce Type: replace-cross Abstract: We consider the problem of support recovery for sparse binary signals from noisy linear measurements. For sparse Gaussian measurement matrice...