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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > New directions in solving structured nonconvex problems in multivariate statistics
New directions in solving structured nonconvex problems in multivariate statisticsAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact INI IT. This talk has been canceled/deleted Nonconvex problems arise frequently in modern applied statistics and machine learning, posing outstanding challenges from a computational and statistical viewpoint. Continuous especially convex optimization, has played a key role in our computational understanding of (relaxations or approximations of) these problems. However, some other well-grounded techniques in mathematical optimization (for example, mixed integer optimization) have not been explored to their fullest potential. When the underlying statistical problem becomes difficult, simple convex relaxations and/or greedy methods have shortcomings. Fortunately, many of these can be ameliorated by using estimators that can be posed as solutions to structured discrete optimization problems. To this end, I will demonstrate how techniques in modern computational mathematical optimization (especially, discrete optimization) can be used to address the canonical problem of best-subset selection and cousins. I will describe how recent algorithms based on local combinatorial optimization can lead to high quality solutions in times comparable to (or even faster than) the fastest algorithms based on L1-regularization. I will also discuss the relatively less understood low Signal to Noise ratio regime, where usual subset selection performs unfavorably from a statistical viewpoint; and propose simple alternatives that rely on nonconvex optimization. If time permits, I will outline problems arising in the context robust statistics (least median squares/least trimmed squares), low-rank factor analysis and nonparametric function estimation where, these techniques seem to be promising. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:This talk is not included in any other list Note that ex-directory lists are not shown. |
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