Bayesian predictive methods for covariate selection in large p small n problems
Details
Directions
Chelsea Market Entrance at 75 Ninth Ave, New York, NY 10011 (BTWN 15th & 16th street) Once you enter the building there are 2 elevators on the immediate right hand side (near Security station) take either elevator up to the 4th floor. Elevators require a badge, so someone from Google will have to escort you & guests to 4th floor. We have Wildwood conf. room for the event.
Introduction
We are lucky to have Aki Vehtari (https://users.aalto.fi/~ave/) from Aalto University in Finland present some of his latest work on priors and Bayesian predictive methods for covariate selection in large p, small n regressions.
Aki is an associate professor in computational science (focus on probabilistic modeling) at Aalto University. He is a co-author of Bayesian Data Analysis book with Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, and Donald B. Rubin.
Abstract
I first present recent development in hierarchical shrinkage priors for presenting sparsity assumptions in covariate effects. I review an easy and intuitive way of setting up the prior for based on our prior beliefs about the number of effectively nonzero coefficients in the model. I also discuss the computational issues when using hierarchical shrinkage priors. I emphasize the separation between prior information on sparsity and decision theoretic approach for selecting a smaller set of covariates having good predictive performance. I briefly review comparison of Bayesian predictive methods for model selection and discuss in more detail projection predictive variable selection ch for regression.
Background
Here is some light, preliminary reading for y'all:
Juho Piironen and Aki Vehtari (2017). On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:905-913.
http://proceedings.mlr.press/v54/piironen17a.html
Juho Piironen and Aki Vehtari (2017). Comparison of Bayesian predictive methods for model selection. Statistics and Computing, 27(3):711-735. doi:10.1007/s11222-016-9649-y.
http://link.springer.com/article/10.1007/s11222-016-9649-y
Aki Vehtari, Andrew Gelman and Jonah Gabry (2016). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. In Statistics and Computing, doi:10.1007/s11222-016-9696-4.
http://link.springer.com/article/10.1007/s11222-016-9696-4
https://arxiv.org/abs/1507.04544
Aki Vehtari and Janne Ojanen (2012). A survey of Bayesian predictive methods for model assessment, selection and comparison. Statistics Surveys, 6:142-228.
