|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Learning rates in Bayesian nonparametrics: Gaussian process priors
If you have a question about this talk, please contact Julia Blackwell.
Joint with Probability Series
The sample path of a Gaussian process can be used as a prior model for an unknown function that we wish to estimate. For instance, one might model a regression function or log density a priori as the sample path of a Brownian motion or its primitive, or some stationary process. Viewing this prior model as a formal prior distribution in a Bayesian set-up, we obtain a posterior distribution in the usual way, which, given the observations, is a probability distribution on a function space.
We study this posterior distribution under the assumption that the data is generated according to some given true function, and are interested in whether the posterior contracts to the true function if the informativeness in the data increases indefinitely, and at what speed.
For Gaussian process priors this rate of contraction rate can be described in terms of the small ball probability of the Gaussian process and the position of the true parameter relative to its reproducing kernel Hilbert space. Typically the prior has a strong influence on the contraction rate. This dependence can be alleviated by scaling the sample paths. For instance, an infinitely smooth, stationary Gaussian process scaled by an inverse Gamma variable yields a prior distribution on functions such that the posterior distribution adapts to the unknown smoothness of the true parameter, in the sense that contraction takes place at the minimax rate for the true smoothness.
This talk is part of the Statistics series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsStatistical Methods for Cognitive Psychologists Physiology, Development and Neuroscience Talks Analysis Seminar
Other talksCan Layout and Engraving Rules Affect the Readability of Musical Scores? Furniture at the Fitz: New arrivals Multi-sensor geophysical constraints on crustal melt in the central Andes at a so-called zombie volcano: the PLUTONS project Mau Mau: The Face of International Terrorism in the 1950's in the Contemporary Perspective' An update on dementia in our older population Respiratory Health and Smoking Science Summit 2016