Biological systems are driven by complex regulatory processes. Graphical models play a crucial role in the analysis and reconstruction of such processes. It is possible to derive regulatory models using network inference algorithms from high-throughput data, for example; from gene or protein expression data. A wide variety of network inference algorithms have been designed and implemented. Our aim is to explore the possibilities of using statistical independence criteria for biological network inference. The contributions of our work can be categorized into four sections. First, we provide a detailed overview of some of the most popular general independence criteria: distance covariance (dCov), kernel canonical variance (KCC), kernel generalized variance (KGV) and the Hilbert-Schmidt Independence Criterion (HSIC). We provide easy to understand geometrical interpretations for these criteria. We also explicitly show the equivalence of dCov, KGV and HSIC. Second, we introduce a new criterion for measuring dependence based on the signal to noise ratio (SNRIC). SNRIC is significantly faster to compute than other popular independence criteria. SNRIC is an approximate criterion but becomes exact under many popular modelling assumptions, for example for data from an additive noise model. Third, we compare the performance of the independence criteria on biological experimental data within the framework of the PC algorithm. Since not all criteria are available in a version that allows for testing conditional independence, we propose and test an approach which relies on residuals and requires only an unconditional version of an independence criterion. Finally we propose a novel method to infer networks with feedback loops. We use an MCMC sampler, which samples using a loss function based on an independence criterion. This allows us to find networks under very general assumptions, such as non-linear relationships, non-Gaussian noise distributions and feedback loops.

Este trabalho fornece uma avaliação empírica do desempenho de Redes Bayesianas quando se impõe restrições à largura de árvore de sua estrutura. O desempenho da rede é visto especificamente pela sua capacidade de generalização e também pela precisão da inferência em problemas de tomada de decisão. Resultados preliminares sugerem que adicionar essa restrição na largura de árvore diminui a capacidade de generalização do modelo além de tornar a tarefa de aprendizado mais difícil. / This work provides an empirical evaluation of the performance of Bayesian Networks when treewidth is bounded. The performance of the network is viewed as its generalizability and also as the accuracy of inference in decision making problems. Preliminary results suggest that adding constraints to treewidth decreases the model performance on unseen data and makes the corresponding optimization problem more difficult.

Este trabalho fornece uma avaliação empírica do desempenho de Redes Bayesianas quando se impõe restrições à largura de árvore de sua estrutura. O desempenho da rede é visto especificamente pela sua capacidade de generalização e também pela precisão da inferência em problemas de tomada de decisão. Resultados preliminares sugerem que adicionar essa restrição na largura de árvore diminui a capacidade de generalização do modelo além de tornar a tarefa de aprendizado mais difícil. / This work provides an empirical evaluation of the performance of Bayesian Networks when treewidth is bounded. The performance of the network is viewed as its generalizability and also as the accuracy of inference in decision making problems. Preliminary results suggest that adding constraints to treewidth decreases the model performance on unseen data and makes the corresponding optimization problem more difficult.