The Theory Of Granger Causality And Its Applications In Systems Biology

One of the most fundamental issues in systems biology is to reliably and accurately explore the network structure of elements (genes, proteins, metabolites, neurons etc.), based upon high throughput data obtained from gene-chips and microar-ray experiments. There are several well-established reverse-engineering approaches to uncover causal relationships in a dynamic network, such as ordinary differential equations (ODE), Bayesian networks, Boolean network and Granger Causality. Here we focuse on the Granger causality approach in both the time and frequency domains.The method of causality was first introduced by Wiener in 1956. Granger formalized this notion in the context of linear vector autoregression (VAR) model of time series in 1969, which was the well-known Granger causality. In 1982, Geweke introduced the notion of conditional Granger causality, which could be used to analyse the interrelationship of multi-dimensional data. Furthermore, he extended time domain Granger causality to frequency domain, obtained the frequency decomposition of Granger causality. From Kolmogrov formula, frequency domain Granger causality was consistent with that in the time domain, which enlarged the applications of Granger causality. In this paper, we introduce some extensions of conditional Granger causalty and test them both in simulated examples and in experimental data. The paper is organized as follows:In chapter 1, we introduce the research background and current research status abroad of this subject in details, we also introduce the structure of this paper.In chapter 2, we introduce the conceptual framework and preliminaries of mathematics and biology of this paper.In chapter 3, we extend conditional Granger causality to a new concept: partial Granger causality. From the comparison of conditional Granger causality and partial Granger causality, we find that partial Granger causality can eliminate the influence of common exogenous inputs and latent variables and explore the true relationship while conditional Granger causality can not.In chapter 4, we analyse partial Granger causality in frequency domain and obtain the frequency decomposition of partial Granger causality which is consistent with that in the time domain.In chapter 5, we extend partial Granger causality again and obtain another concept: partial complex Granger causality, which can be used to uncover the interaction of complexes. We present corresponding frequency decomposition of it meanwhile.Because traditional Granger causality is only suitable for dealing with the cases of small network, in chapter 6, we present an effective algorithm for big network: hierarchical partial Granger causality. We find that our algorithm is robust for dealing with both simulated examples and experimental recordings.In the last chapter, we make some conclusions of our research work and put forward some relative problems which we will go ahead.