Causal vs. Anticausal merging of predictors

Sergio Hernan Garrido Mejia, Patrick Blöbaum, Bernhard Schölkopf, Dominik Janzing

Keywords: Causality, Merging of predictors, Causal vs Anticausal, Maximum Entropy

TL;DR: We study the asymmetries produced in the merging of predictors whenever we have causal information.

Abstract:

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.

Primary Area: Causal inference

Submission Number: 18529