Unate distributions require θ̃(n^{3/2}) samples for uniformity testing and allow Õ(n^{3/2}) conditional samples for unateness testing in the subcube model.
Various thresholds for $\ell_1$-optimization in compressed sensing
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
Recently, \cite{CRT,DonohoPol} theoretically analyzed the success of a polynomial $\ell_1$-optimization algorithm in solving an under-determined system of linear equations. In a large dimensional and statistical context \cite{CRT,DonohoPol} proved that if the number of equations (measurements in the compressed sensing terminology) in the system is proportional to the length of the unknown vector then there is a sparsity (number of non-zero elements of the unknown vector) also proportional to the length of the unknown vector such that $\ell_1$-optimization succeeds in solving the system. In this paper, we provide an alternative performance analysis of $\ell_1$-optimization and obtain the proportionality constants that in certain cases match or improve on the best currently known ones from \cite{DonohoPol,DT}.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
This review synthesizes representative advances in high-dimensional statistics, highlights common themes and open problems, and points to key entry works.
citing papers explorer
-
Testing Unate Distributions
Unate distributions require θ̃(n^{3/2}) samples for uniformity testing and allow Õ(n^{3/2}) conditional samples for unateness testing in the subcube model.
-
High-Dimensional Statistics: Reflections on Progress and Open Problems
This review synthesizes representative advances in high-dimensional statistics, highlights common themes and open problems, and points to key entry works.