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We study the problem of consistently recovering the sparsity pattern of aregression parameter vector from correlated observations governed bydeterministic missing data patterns using Lasso. We consider the case in whichthe observed dataset is censored by a deterministic, non-uniform filter.Recovering the sparsity pattern in datasets with deterministic missingstructure can be arguably more challenging than recovering in auniformly-at-random scenario. In this paper, we propose an efficient algorithmfor missing value imputation by utilizing the topological property of thecensorship filter. We then provide novel theoretical results for exact recoveryof the sparsity pattern using the proposed imputation strategy. Our analysisshows that, under certain statistical and topological conditions, the hiddensparsity pattern can be recovered consistently with high probability inpolynomial time and logarithmic sample complexity.

Provable Guarantees for Sparsity Recovery with Deterministic Missing Data Patterns