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• W1729367118 abstract "Variable selection for sparse linear regression is the problem of finding, given an m p matrix B and a target vector y, a sparse vector x such that Bx approximately equals y. Assuming a standard complexity hypothesis, we show that no polynomial-time algorithm can find ak 0 -sparse x withkBx yk 2 h(m;p), wherek 0 = k 2 log 1 p andh(m;p) = p C1 m 1 C2 , where > 0;C1 > 0;C2 > 0 are arbitrary. This is true even under the promise that there is an unknownk-sparse vector x satisfyingBx = y. We prove a similar result for a statistical version of the problem in which the data are corrupted by noise. To the authors’ knowledge, these are the first hardness results for sparse regression that apply when the algorithm simultaneously hask 0 > k andh(m;p) > 0." @default.
• W1729367118 created "2016-06-24" @default.
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• W1729367118 date "2015-06-26" @default.
• W1729367118 modified "2023-09-23" @default.
• W1729367118 title "Variable Selection is Hard" @default.
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