Robust and Parallel Bayesian Model Selection

Effective and accurate model selection that takes into account model uncertainty is an important but challenging problem in modern data analysis. One of the major challenges is the computational burden required to infer huge data sets which, in general, cannot be stored or processed on one machine. Moreover, in many real data modeling scenarios we may encounter the presence of outliers and contaminations that will damage the quality of our model and variable selection. We can overcome both of these problems through a simple "divide and conquer" strategy in which we divide the observations of the full data set equally into subsets and perform inference and model selections independently on each subset. After local subset inference, we can aggregate the optimal subset model or aggregate the local model/variable selection criteria to obtain a final model. We show that by aggregating with the geometric median, we obtain results that are robust to outliers and contamination of an unknown nature.