Microbiome dynamics analysis using a novel multivariate vector autoregression model with weighted fusion regularization

In recent years, there are growing interests in developing novel approaches for inferring dynamic interactions in biological systems including gene transcription network and microbial interaction networks. Multivariate Vector Autoregression (MVAR) model is one of these efficient methods. Variants of MVAR with different penalties or regularizations can avoid the problem of over-fitting and provide great potential in high-dimensional data analysis. In this paper, we developed a novel regularization methods for MVAR via weighted fusion which consider the correlation among variables. The weighted fusion can potentially incorporate information redundancy among correlated variables for estimation and variable selection. Weighted fusion is also useful when the number of predictors p is larger than the number of observations n. In theory, we discuss the grouping effect of weighted fusion regularization for linear models. We then apply the proposed model 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 that several other VAR-based models and we demonstrate its capability of extracting relevant microbial interactions.