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Clustering with Queries under Semi-Random Noise
Our main result is a computationally efficient algorithm that can identify large clusters with $O\left(\frac{nk \log n} {(1-2p)^2}\right) + \text{poly}\left(\log n, k, \frac{1}{1-2p} \right)$ queries, matching the guarantees of the best known algorithms in the fully-random model.
Sparse PCA on fixed-rank matrices
Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components.
Subset selection in sparse matrices
In subset selection we search for the best linear predictor that involves a small subset of variables.
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