Leo Breiman, the Rashomon Effect, and the Occam Dilemma

Abstract: In the famous Two Cultures paper, Leo Breiman provided a visionary perspective on the cultures of ''data models'' (modeling with consideration of data generation) versus ''algorithmic models'' (vanilla machine learning models). I provide a modern perspective on these approaches. One of Breiman's key arguments against data models is the ''Rashomon Effect,'' which is the existence of many different-but-equally-good models. The Rashomon Effect implies that data modelers would not be able to determine which model generated the data. Conversely, one of his core advantages in favor of data models is simplicity, as he claimed there exists an ''Occam Dilemma,'' i.e., an accuracy-simplicity tradeoff. After 25 years of powerful computers, it has become clear that this claim is not generally true, in that algorithmic models do not need to be complex to be accurate; however, there are nuances that help explain Breiman's logic, specifically, that by ''simple,'' he appears to consider only linear models or unoptimized decision trees. Interestingly, the Rashomon Effect is a key tool in proving the nullification of the Occam Dilemma. To his credit though, Breiman did not have the benefit of modern computers, with which my observations are much easier to make. Breiman's goal for interpretability was somewhat intertwined with causality: simpler models can help reveal which variables have a causal relationship with the outcome. However, I argue that causality can be investigated without the use of single models, whether or not they are simple. Interpretability is useful in its own right, and I think Breiman knew that too. Technically, my modern perspective does not belong to either of Breiman's Two Cultures, but shares the goals of both of them - causality, simplicity, accuracy - and shows that these goals can be accomplished in other ways, without the limitations Breiman was concerned about.