In sparse recovery with mixed-quality data, the information-theoretic price of quality is bounded by two in the agnostic decoder case but can grow arbitrarily large when informed, while LASSO recovery depends only on average noise level.
(34) Similarly to (34), we obtain the following expression forM −∆2 i (θ): M−∆2 i (θ) = 1q 1−2|U∪V| (−θ+2θ2σ2
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Price of Quality: Sufficient Conditions for Sparse Recovery using Mixed-Quality Data
In sparse recovery with mixed-quality data, the information-theoretic price of quality is bounded by two in the agnostic decoder case but can grow arbitrarily large when informed, while LASSO recovery depends only on average noise level.