Network Inference Using Independence Criteria

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Verbyla, Petras 

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.

Wernisch, Lorenz
Independence Criteria, MCMC, Network Inference, Kernels, Bayesian Networks, PC Algorithm, Loss Function
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge