Robust and Parallel Bayesian Model Selection
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Effective and accurate model selection is an important problem in modern data analysis. One of the major challenges is the computational burden required to handle large data sets that cannot be stored or processed on one machine. Another challenge one may encounter is the presence of outliers and contaminations that damage the inference quality. In this paper, we extend the recently studied "divide and conquer" strategy in Bayesian parametric inference to the model selection context, in which we divide the observations of the full data set into roughly equal subsets and perform inference and model selection independently on each subset. After local subset inference, we aggregate the posterior model probabilities or other model/variable selection criteria to obtain a final model, by using the notion of geometric median. We show how this approach leads to improved concentration in finding the "correct" model and also parameters, and how it is robust to outliers and data contamination.
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