High-dimensional linear state space models for dynamic microbial interaction networks.

Medical researchers are increasingly interested in knowing how the complex community of micro-organisms living on human body impacts human health. Key to this is to understand how the microbes interact with each other. Time-course studies on human microbiome indicate that the composition of microbiome changes over short time periods, primarily as a consequence of synergistic and antagonistic interactions of the members of the microbiome with each other and with the environment. Knowledge of the abundance of bacteria-which are the predominant members of the human microbiome-in such time-course studies along with appropriate mathematical models will allow us to identify key dynamic interaction networks within the microbiome. However, the high-dimensional nature of these data poses significant challenges to the development of such mathematical models. We propose a high-dimensional linear State Space Model (SSM) with a new Expectation-Regularization-Maximization (ERM) algorithm to construct a dynamic Microbial Interaction Network (MIN). System noise and measurement noise can be separately specified through SSMs. In order to deal with the problem of high-dimensional parameter space in the SSMs, the proposed new ERM algorithm employs the idea of the adaptive LASSO-based variable selection method so that the sparsity property of MINs can be preserved. We performed simulation studies to evaluate the proposed ERM algorithm for variable selection. The proposed method is applied to identify the dynamic MIN from a time-course vaginal microbiome study of women. This method is amenable to future developments, which may include interactions between microbes and the environment.