NARMAX model as a sparse, interpretable and transparent machine learning approach for big medical and healthcare data analysis

Influenza and influenza-like illnesses are one of the leading causes of death in the world, resulting in heavy losses to individual families and nations. Accurate and timely forecasts of seasonal influenza would therefore crucially important to inform and facilitate public health decision-making for presenting and intervening influenza epidemics. System identification and data-driven modelling approaches play an indispensable role in analyzing and understanding complex processes including medical, healthcare and environmental time series. This paper aims to present a type of sparse, interpretable and transparent (SIT) model, which cannot only be used for future behavior prediction but more importantly for understanding the dependent relationship between the response variables of a system on potential independent variables (also known as input variables or predictors). An ideal candidate for such a SIT representation is the well-known NARMAX (nonlinear autoregressive moving average with exogenous inputs) model, which can be established based on input and output data of the system of interest, and the final refined model is usually simple, parsimonious and easy to interpret. The general framework of the NARMAX model is presented, and the state-of-the-art algorithms for such a SIT model estimation are described. Two case studies are provided to illustrate how well the SIT-NARMAX model can work for medical, healthcare and related data.