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Veronika Rockova — University of Chicago
Friday 15 November 2019, 14:00-15:00
Multiscale Analysis of Bayesian CART
- 👤 Speaker: Veronika Rockova — University of Chicago
- 📅 Date & Time: Friday 15 November 2019, 14:00 - 15:00
- 📍 Venue: MR12
Abstract
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)
Series This talk is part of the Statistics series.
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