Time-penalised trees (TpT): introducing a new tree-based data mining algorithm for time-varying covariates

Abstract

This article introduces a new decision tree algorithm that accounts for time-varying covariates in the decision-making process. Traditional decision tree algorithms assume that the covariates are static and do not change over time, which can lead to inaccurate predictions in dynamic environments. Other existing methods suggest workaround solutions such as the pseudo-subject approach, discussed in the article. The proposed algorithm utilises a different structure and a time-penalised splitting criterion that allows a recursive partitioning of both the covariates space and time. Relevant historical trends are then inherently involved in the construction of a tree, and are visible and interpretable once it is fit. This approach allows for innovative and highly interpretable analysis in settings where the covariates are subject to change over time. The effectiveness of the algorithm is demonstrated through a real-world data application in life insurance. The results presented in this article can be seen as an introduction or proof-of-concept of our time-penalised approach, and the algorithm’s theoretical properties and comparison against existing approaches on datasets from various fields, including healthcare, finance, insurance, environmental monitoring, and data mining in general, will be explored in forthcoming work.