Bayesian Analysis of Risk for Data Mining Based on Empirical Likelihood

We consider an approximate posterior approach to making joint probabilistic inference on the action and the associated risk in data mining. The posterior probability is based on a profile empirical likelihood, which imposes a moment restriction relating the action to the resulting risk, but does not otherwise require a probability model for the underlying data generating process. The moment restriction partially but not fully identifies the parameters of interest, which include both the theoretical risk and the associated actions. We illustrate with examples how this framework can be used to describe the EL-posterior probability of actions to take in order to achieve a low risk, or conversely, to describe the posterior distribution of the resulting risk for a given action. A theoretic study on the frequentist properties reveals that the EL-posterior clusters around the true risk-action relation with high probability for large data size, and that the actions can be generated from this posterior to reliably control the true resulting risk. Finally, an application to the German credit data is presented