Predicting microbial interactions by using network-constrained regularization incorporating covariate coefficients and connection signs

Network is an exceptional way of depicting biological information. In biology, many different biological processes are represented by network, such as regulatory network, metabolic network and food web. In biology, network is a powerful supplement to the standard numerical data such as profile or count data. By absorbing network information, Vector autoregressive (VAR) model was proved to be an efficient approach to infer dynamic interactions in biological systems. Variants of network-regularized VAR with different penalties or regularization can avoid the problem of over-fitting and provide great potential in high-dimensional time series analysis. In this paper, we develop a novel regularization method for multivariate VAR which incorporates not only network topology but the signs of the network connections. By virtue of coordinate descent, we present a fast implementation for estimating model parameters. We then apply the proposed approach on several time series data sets especially a time series dataset of human gut microbiomes. The experimental results indicate that the new approach has better performance than other VAR-based models.