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• W2166000574 abstract "We consider the problem of estimating the support of a vector $beta^* in mathbb{R}^{p}$ based on observations contaminated by noise. A significant body of work has studied behavior of $ell_1$-relaxations when applied to measurement matrices drawn from standard dense ensembles (e.g., Gaussian, Bernoulli). In this paper, we analyze emph{sparsified} measurement ensembles, and consider the trade-off between measurement sparsity, as measured by the fraction $gamma$ of non-zero entries, and the statistical efficiency, as measured by the minimal number of observations $n$ required for exact support recovery with probability converging to one. Our main result is to prove that it is possible to let $gamma to 0$ at some rate, yielding measurement matrices with a vanishing fraction of non-zeros per row while retaining the same statistical efficiency as dense ensembles. A variety of simulation results confirm the sharpness of our theoretical predictions." @default.
• W2166000574 created "2016-06-24" @default.
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• W2166000574 date "2008-05-20" @default.
• W2166000574 modified "2023-09-27" @default.
• W2166000574 title "High-dimensional subset recovery in noise: Sparsified measurements without loss of statistical efficiency" @default.
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