Causal vs. Anticausal merging of predictors
This work addresses theoretical asymmetries in predictor merging for causal inference, with implications for out-of-variable generalization, but is incremental as it builds on existing causal methods.
The paper investigates differences in merging predictors in causal versus anticausal directions using a simple model with binary target and continuous predictors, showing that Causal Maximum Entropy reduces to logistic regression in the causal direction and Linear Discriminant Analysis in the anticausal direction when all bivariate distributions are observed.
We study the differences arising from merging predictors in the causal and anticausal directions using the same data. In particular we study the asymmetries that arise in a simple model where we merge the predictors using one binary variable as target and two continuous variables as predictors. We use Causal Maximum Entropy (CMAXENT) as inductive bias to merge the predictors, however, we expect similar differences to hold also when we use other merging methods that take into account asymmetries between cause and effect. We show that if we observe all bivariate distributions, the CMAXENT solution reduces to a logistic regression in the causal direction and Linear Discriminant Analysis (LDA) in the anticausal direction. Furthermore, we study how the decision boundaries of these two solutions differ whenever we observe only some of the bivariate distributions implications for Out-Of-Variable (OOV) generalisation.