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We study the problem of exact support recovery: given an (unknown) vector$\theta \in \left\{-1,0,1\right\}^D$, we are given access to the noisymeasurement $$ y = X\theta + \omega,$$ where $X \in \mathbb{R}^{N \times D}$ isa (known) Gaussian matrix and the noise $\omega \in \mathbb{R}^N$ is an(unknown) Gaussian vector. How small we can choose $N$ and still reliablyrecover the support of $\theta$? We present RAWLS (Randomly AggregatedUnWeighted Least Squares Support Recovery): the main idea is to take randomsubsets of the $N$ equations, perform a least squares recovery over thisreduced bit of information and then average over many random subsets. We showthat the proposed procedure can provably recover an approximation of $\theta$and demonstrate its use in support recovery through numerical examples.

Randomly Aggregated Least Squares for Support Recovery