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Strong converses and high-dimensional statistical estimation problems

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MQIW05 - Beyond I.I.D. in information theory

In many statistical inference problems, we wish to bound the performance of any possible estimator. This can be seen as a converse result, in a standard information-theoretic sense. A standard approach in the statistical literature is based on Fano’s inequality, which typically gives a weak converse. We adapt these arguments by replacing Fano by more recent information-theoretic ideas, based on the work of Polyanskiy, Poor and Verdu. This gives tighter lower bounds that can be easily computed and are asymptotically sharp. We illustrate our technique in three applications: density estimation, active learning of a binary classifier, and compressed sensing, obtaining tighter risk lower bounds in each case.  

(joint with Oliver Johnson, see doi:10.1214/18-EJS14)




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