Bayesian network structural learning from complex survey data: a resampling based approach

Nowadays there is increasing availability of good quality official statistics data. The construction of multivariate statistical models possibly leading to the identification of causal relationships is of interest. In this context Bayesian networks play an important role. A crucial step consists in learning the structure of a Bayesian network. One of the most widely used procedures is the PC algorithm consisting in carrying out several independence tests on the available data set and in building a Bayesian network according to the tests results. The PC algorithm is based on the irremissible assumption that data are independent and identically distributed. Unfortunately, official statistics data are generally collected through complex sampling designs, then the aforementioned assumption is not met. In such a context the PC algorithm fails in learning the structure. To avoid this, the sample selection must be taken into account in the structural learning process. In this paper, a modified version of the PC algorithm is proposed for inferring causal structure from complex survey data. It is based on resampling techniques for finite populations. A simulation experiment showing the robustness with respect to departures from the assumptions and the good performance of the proposed algorithm is carried out.