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We formulate sparse support recovery as a salient set identification problemand use information-theoretic analyses to characterize the recovery performanceand sample complexity. We consider a very general model where we are notrestricted to linear models or specific distributions. We state non-asymptoticbounds on recovery probability and a tight mutual information formula forsample complexity. We evaluate our bounds for applications such as sparselinear regression and explicitly characterize effects of correlation or noisyfeatures on recovery performance. We show improvements upon previous work andidentify gaps between the performance of recovery algorithms and fundamentalinformation.

Sparse Recovery with Linear and Nonlinear Observations: Dependent and Noisy Data