Refined Least Squares for Support Recovery
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We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement y = Xθ^* + ω, and X∈ℝ^N × D which is a (known) Gaussian matrix and ω∈ℝ^N is an (unknown) Gaussian noise vector, our goal is to recover the support of the (unknown) sparse vector θ^* ∈{-1,0,1}^D. To recover the support of the θ^* we use an average of multiple least squares solutions, each computed based on a subset of the full set of equations. The support is estimated by identifying the most significant coefficients of the average least squares solution. We demonstrate that in a wide variety of settings our method outperforms state-of-the-art support recovery algorithms.
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