Sparsity pattern aggregation for convex stochastic optimization.
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Important statistical problems including regression, binary classification
and density estimation can be recast as convex stochastic optimization
problems when seen from the point of view of statistical aggregation. These
convex problems can be numerically solved efficiently in high dimension but
may show mediocre statistical performance. One way to overcome this
situation consists in assuming that there exists approximate solution,
called “sparse”, that are of moderate dimension. This presentation
introduces a new method called “exponential screening (ES)” as an
alternative to the $\ell_1$-penalization idea, which is currently the most
popular way to find these sparse solutions. While $\ell_1$ based methods can
be analyzed only under rather stringent assumptions, ES shows optimal
statistical performance under fairly general assumptions. Implementation is
not straightforward but it can be approximated using the Metropolis
algorithm which results in a stochastic greedy algorithm and performs
surprisingly well in a simulated problem of sparse recovery.
http://www.princeton.edu/~rigollet/index.html
This talk is part of the Statistics series.
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