Computation of Kullback-Leibler Divergence in Bayesian Networks.

Kullback-Leibler divergence KL(p,q) is the standard measure of error when we have a true probability distribution which is approximate with probability distribution . Its efficient computation is essential in many tasks, as in approximate computation or as a measure of error when learning a probability. In high dimensional probabilities, as the ones associated with Bayesian networks, a direct computation can be unfeasible.

Combining gene expression data and prior knowledge for inferring gene regulatory networks via Bayesian networks using structural restrictions.

Gene Regulatory Networks (GRNs) are known as the most adequate instrument to provide a clear insight and understanding of the cellular systems. One of the most successful techniques to reconstruct GRNs using gene expression data is Bayesian networks (BN) which have proven to be an ideal approach for heterogeneous data integration in the learning process. Nevertheless, the incorporation of prior knowledge has been achieved by using prior beliefs or by using networks as a starting point in the search process.

Increasing power by using haplotype similarity in a multimarker transmission/disequilibrium test.

It is already known that power in multimarker transmission/disequilibrium tests may improve with the number of markers as some associations may require several markers to be captured. However, a mechanism such as haplotype grouping must be used to avoid incremental complexity with the number of markers. 2G, a state-of-the-art transmission/disequilibrium test, implements this mechanism to its maximum extent by grouping haplotypes into only two groups, high and low-risk haplotypes, so that the test has only one degree of freedom regardless of the number of markers.

A method for integrating expert knowledge when learning Bayesian networks from data.

Automatic learning of Bayesian networks from data is a challenging task, particularly when the data are scarce and the problem domain contains a high number of random variables. The introduction of expert knowledge is recognized as an excellent solution for reducing the inherent uncertainty of the models retrieved by automatic learning methods. Previous approaches to this problem based on Bayesian statistics introduce the expert knowledge by the elicitation of informative prior probability distributions of the graph structures.