Granger Lasso Causal Models in Higher Dimensions - Application to Gene Expression Regulatory Networks

Granger causality (GC), based on a vector autoregressive model, is one of the most popular methods in uncovering the temporal dependencies among time series. The original Granger model is able to detect only linear causal dependencies and many approaches were recently developed to extend it to the non-linear modeling. The method Copula-Granger from Bahadori and Liu in 2012 introduces non-linearity into the causality modeling by representing the data distribution by copulas. The detection of causality of gene regulatory networks (GRN) from experimental data, such as gene expression measurements, is a challenging problem, being solved by various computational methods with various success. We applied the Granger Lasso method, the Copula Granger method and the combination of dynamic Bayesian Networks with ordinary differential equation method (ODE-DBN) to cell division cycle gene expression data from the human cancer cell line (HeLa) for a regulatory network of 19 selected genes. We tested the causal detection ability of the methods with respect to the selected benchmark network. We compared the performance of the mentioned methods or various statistical measures. All three methods are scalable and can be easily extended to higher dimensions. The results of both Granger Lasso and Copula Granger outperformed the ODE-DBN both in terms of precision and the computational time. We conclude that the DBN combined with ODE method are not feasible for large GRN because of the computational intensity of the methods and surprisingly low precision. This type of methods is more feasible for modeling of local dynamics within a small genetic regulatory networks, rather than for detection of causal relationships in a large genetic regulatory network. We believe that the assumption of Gaussian processes, on which are DBN based, is in larger genetic regulatory networks violated.