Randomly Aggregated Least Squares for Support Recovery

03/16/2020

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by   Ofir Lindenbaum, et al.

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We study the problem of exact support recovery: given an (unknown) vector θ∈{-1,0,1}^D, we are given access to the noisy measurement y = Xθ + ω, where X ∈R^N × D is a (known) Gaussian matrix and the noise ω∈R^N is an (unknown) Gaussian vector. How small we can choose N and still reliably recover the support of θ? We present RAWLS (Randomly Aggregated UnWeighted Least Squares Support Recovery): the main idea is to take random subsets of the N equations, perform a least squares recovery over this reduced bit of information and then average over many random subsets. We show that the proposed procedure can provably recover an approximation of θ and demonstrate its use in support recovery through numerical examples.