Title: Bayesian predictive inference in decomposable graphs using sequential Monte Carlo samplers
Authors: Felix Rios - KTH Royal Institute of Technology (Sweden)
Tetyana Pavlenko - KTH Royal Institute of Technology (Sweden) [presenting]
Abstract: Bayesian predictive inference in the class of decomposable graphical models is considered within the classification framework. We present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model determination into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emphasis is then placed on the Bayesian model averaging which takes full account of the class-specific model uncertainty by averaging over the posterior graph model probabilities. Even though the decomposability assumption severely reduces the model space, the size of the class of decomposable models is still immense, rendering the explicit Bayesian averaging over all the models infeasible. To address this issue, we consider the particle Gibbs strategy for posterior sampling from decomposable graphical models which utilize the Christmas tree algorithm as proposal kernel. We also derive the strong hyper Markov law which we call the hyper normal Wishart law that allows to perform the resultant Bayesian inference locally. The proposed predictive graphical classifier reveals superior performance compared to the ordinary Bayesian predictive rule that does not account for the model uncertainty, as well as to a number of out-of-the-box classifiers.