Comment on 'Statistical Modelling: the Two Cultures' by Leo Breiman

Abstract

The discussion paper "Statistical Modeling: the Two Cultures" (Statistical Science, Vol 16, 2001) by the late Leo Breiman sent shockwaves throughout the statistical community and subsequently redirected the efforts of much of the field towards machine learning, highdimensional analysis and data mining approaches. In this discussion, we discuss some of the implications of this work in the sphere of causal inference. In particular, we define the concept of comparability, which is fundamental to the ability to draw causal inferences and reinterpret some concepts in high-dimensional data analysis from this viewpoint. One of the points we highlight in this discussion is the need to consider data-adaptive estimands for causal effects with high-dimensional confounders. We also revisit matching and develop some mathematical formalism for matching algorithms.