How weather conditions affect the spread of Covid-19 : findings from a study using contrastive learning and NARMAX models

Machine learning (ML) has demonstrated a powerful ability in learning complex patterns or inherent dynamics from observed data. Most machine learning models are black-box, in that the internal behaviour of the models is opaque and thus unknown to no one. However, in many real applications, e.g., in many medical and healthcare domains, it is significantly useful or necessary to explicitly know the internal compositions, combinations or interactions of the models to be used for one purpose or another. Therefore, the interest in interpreting machine learning models has increasingly grown in recent years, especially for cases where users need to do predictions using the models and require explanations for an insightful understanding of drivers that cause the predicted behaviour. This study introduces a novel interpretable machine learning method based on contrastive learning and Non-linear AutoRegressive Moving Average with eXogenous inputs (NARMAX) model (referred to as CL-NARMAX thereafter). The proposed method provides a glass-box model, where the input-output relationship and interactions between the input variables can be written down, so as the model cannot only be applied for predicting future behaviour but also for explaining the relevant “reasons” behind the predicted behaviour. Two case studies are provided to illustrate the usability and performance of the proposed CL-NARMAX approach. The first case study focuses on modelling and analyzing weather conditions against the Covid-19 data in the UK and France, aiming to reveal the impacts of climatic factors on the spread of Covid-19 using the proposed CL-NARMAX method. The second case study focuses on modelling the relationship between influenza-like illness (ILI) incidence rate and the relevant mortality based on the England data, where it is mainly served for illustration purpose, showing how CL-NARMAX is used to model a dynamic system, generating dynamic process models that can be used for explanation and prediction.