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Title: Statistical and Computational Tradeoffs in High Dimensional Learning


With the recentdata revolution, statisticians are considering larger datasets, more sophisticated models, more complex problems. As a consequence, the algorithmic aspect of statistical methods can no longer be neglected in a world where computational power is the bottleneck, not the lack of observations. In this context, we will establish fundamental limits in the statistical performance of computationally efficient procedures, for the problem of sparse principal component analysis. We will show how it is achieved through average-case reduction to the planted clique problem, and introduce further areas of research in this promising field.