Title: Expectation propagation for generalised quantile regression models
Authors: Mauro Bernardi - University of Padova (Italy) [presenting]
Abstract: $L_\alpha$--quantile regression models generalise quantiles ($\alpha=1$) and expectiles ($\alpha=2$) regression to account for the whole conditional distribution of the response variable. We introduce the $L_\alpha$--quantile regression model and we present a new Bayesian estimation framework where regression parameters are learned by minimising the expected tilted check function. An approximated model evidence is obtained by employing the Expectation Propagation (EP) algorithm. The analytically intractable integration required by the parameters learning problem is solved by minimising the Kullback--Leibler divergence between the unnormalised posterior and a suitable approximating distribution usually belonging to the exponential family. We also provide some theoretical results concerning the consistency of the posterior distribution of the regression parameters under general priors. Moreover, the model selection problem is approached through an approximated Stochastic Search Variable Selection (SSVS--EP) algorithm based on the spike--and--slab prior. The effectiveness of the proposed model and parameter learning method are assessed on synthetic and real datasets.