Inference and Verification of Probabilistic Graphical Models from High-Dimensional Data

Probabilistic graphical modelling technique has been widely used to infer the causal relations in the network from high-dimensional data. One of the most challenging biological questions is the inference and verification of biological network, for example, gene regulatory network and signaling pathway, from high-dimensional omics data. Conditionally dependent genes and undirected network can be inferred from the independently and identically distributed static data, while the time series data can help reconstruct a directed network which is more important to our understanding of the complex biological system. Due to the curse of dimensionality and network sparsity, statistical inference algorithm alone is not efficient and realistic to infer and verify large networks. In this work, we propose a novel technique, which applies the dimensionality reduction, network inference and formal verification methods together to reconstruct some regulatory networks from the static and time-series microarray data. A graphical lasso algorithm is first applied to learn the structure of Gaussian graphical models from static data and infer some conditionally dependent genes. Then, an extended dynamic Bayesian network method is applied to reconstruct some weighted and directed networks from the time series data of selected genes, and also generate symbolic model verification code for model checking. Finally, we apply this technique to reconstruct and verify some regulatory networks in yeast and prostate cancer in response to stress and irradiation respectively for illustration.