Assuming a k-partite planted clique conjecture, the authors prove tight k-to-k^2 sample-complexity lower bounds for robust sparse mean estimation, semirandom community recovery, and a universal class of sparse mixture problems.
Robust estimators in high dimensions wit hout the computational intractability
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Average-Case Lower Bounds for Learning Sparse Mixtures, Robust Estimation and Semirandom Adversaries
Assuming a k-partite planted clique conjecture, the authors prove tight k-to-k^2 sample-complexity lower bounds for robust sparse mean estimation, semirandom community recovery, and a universal class of sparse mixture problems.