Title: Regression modelling with I-priors
Authors: Wicher Bergsma - London School of Economics (United Kingdom) [presenting]
Abstract: The I-prior modelling approach for regression with multiple, possibly multidimensional covariates, and with possible interaction effects, is introduced. The I-prior is a maximum entropy Gaussian prior for the regression function, with covariance function proportional to the Fisher information on the regression function. The proposed approach is a general, practical, methodology unifying a variety of models, including multilevel, varying coefficient, longitudinal, and multidimensional or functional response models. In contrast to Gaussian process regression, a simple EM algorithm can be constructed for I-prior models. This is especially important when there are many hyperparameters, when direct optimization of the marginal likelihood may be difficult. The approach has high model parsimony, in particular for models involving many interaction effects. As a consequence of this model parsimony, we obtain a simple semi-Bayes methodology for selecting interaction effects. Whereas in previous approaches the reproducing kernel Hilbert space framework was adequate, in the I-prior approach it is necessary to consider regression functions in a reproducing kernel Krein space.