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Multiscale Analysis of Bayesian CART

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  • UserVeronika Rockova — University of Chicago
  • ClockFriday 15 November 2019, 14:00-15:00
  • HouseMR12.

If you have a question about this talk, please contact Dr Sergio Bacallado .

This paper affords new insights about Bayesian CART in the context of structured wavelet shrinkage. We show that practically used Bayesian CART priors lead to adaptive rate-minimax posterior concentration in the supremum norm in Gaussian white noise, performing optimally up to a logarithmic factor. To further explore the benefits of structured shrinkage, we propose the g-prior for trees, which departs from the typical wavelet product priors by harnessing correlation induced by the tree topology. Building on supremum norm adaptation, an adaptive non-parametric Bernstein–von Mises theorem for Bayesian CART is derived using multi- scale techniques. For the fundamental goal of uncertainty quantification, we construct adaptive confidence bands with uniform coverage for the regression function under self-similarity. (Joint work with Ismael Castillo)

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