Tag
The paper addresses restricted eigenvalue bounds for heavy-tailed designs, showing that the Gaussian width law fails and introducing threshold occupancy as a critical factor. It derives sharp sample complexity results under isotropic heavy-tailed distributions.
This paper introduces Fisher width and inverse-Fisher width on statistical manifolds, studying their roles in local learning bounds and anisotropic recovery. It proves a complementary relation between the two widths and obtains recovery estimates based on Fisher geometry.
Introduces Fisher width, a Riemannian analogue of Gaussian width for statistical manifolds, which captures local statistical curvature and is invariant under reparameterization. The paper develops its theory, proves generalization bounds for Fisher-Lipschitz classes, and demonstrates computable estimators on MNIST.