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Chaining and convexity

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If you have a question about this talk, please contact Quentin Berthet.

Classical estimates on the suprema of random processes in terms of metric entropy have found widespread use in probability theory, statistics, computer science, and other areas. Such estimates are powerful and easy to use, but often fail to be sharp. To obtain sharp bounds, one must replace these methods by a multiscale analogue known as the generic chaining that was developed by Talagrand. Unfortunately, the latter is notoriously difficult to use in any given situation. In this talk, I will show how convex optimization can be used as an engine to generate multiscale approximations. This provides a general-purpose tool for bounding the suprema of random processes that can be almost as easy to use as classical entropy estimates, but that nonetheless produces sharp results in various interesting situations where classical methods are known to fail.

This talk is part of the Statistics series.

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