Representation Multiplicity in Causal Forests

Abstract

Including covariates alongside strictly monotone transformations can change a causal forest's treatment decisions without adding information. Random feature selection favors covariates represented by these multiple columns. Under stated conditions, I show that this imbalance can persist as samples grow. Treatment effect components associated with other covariates are omitted, attenuated, or recovered depending on their inclusion probabilities and tree depth. Simulations and a job-training replication illustrate sensitivity to redundant transformations. Sampling groups of variables that generate identical splits restores prediction invariance on the grouping data when fitting and randomization are held fixed.