Statistically reinforced machine learning for nonlinear patterns and variable interactions

Abstract

Most statistical models assume linearity and few variable interactions, even though real‐world ecological patterns often result from nonlinear and highly interactive processes. We here introduce a set of novel empirical modeling techniques which can address this mismatch: statistically reinforced machine learning. We demonstrate the behaviors of three techniques (conditional inference tree, model‐based tree, and permutation‐based random forest) by analyzing an artificially generated example dataset that contains patterns based on nonlinearity and variable interactions. The results show the potential of statistically reinforced machine learning algorithms to detect nonlinear relationships and higher‐order interactions. Estimation reliability for any technique, however, depended on sample size. The applications of statistically reinforced machine learning approaches would be particularly beneficial for investigating (1) novel patterns for which shapes cannot be assumed a priori, (2) higher‐order interactions which are often overlooked in parametric statistics, (3) context dependency where patterns change depending on other conditions, (4) significance and effect sizes of variables while taking nonlinearity and variable interactions into account, and (5) a hypothesis using parametric statistics after identifying patterns using statistically reinforced machine learning techniques.