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Abstract:
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Among his many contributions, Blackwell made seminal contributions to information theory and statistics, including early work on characterizing the capacities of various channels. The notion of channel capacity has a natural analogue for statistical problems, where it underlies the characterization of minimax rates of estimation. Inspired by this seminal work, this talk is devoted to the use of information-theoretic methods for tackling statistical questions, and we provide two vignettes. First, in the realm of privacy-aware statistics, how to characterize the tradeoffs between preserving privacy and retaining statistical utility? Second, in the realm of statistical optimization, how can we characterize the fundamental limits of dimensionality reduction methods?
This lecture will draw on joint works with John Duchi, Michael Jordan, and Mert Pilanci.
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