Weighted fusion regularisation and predicting microbial interactions with vector autoregressive model

In this paper, we develop a novel regularisation method for MVAR via weighted fusion which considers the correlation among variables. In theory, we discuss the grouping effect of weighted fusion regularisation for linear models. By virtue of the probability method, we show that coefficients corresponding to highly correlated predictors have small differences. A quantitative estimate for such small differences is given regardless of the coefficients signs. The estimate is also improved when consider empirical approximation error if the model fit the data well. 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 than several other VAR-based models and we also demonstrate its capability of extracting relevant microbial interactions.