Poster
Causal vs. Anticausal merging of predictors
Sergio Garrido Mejia · Patrick Blöbaum · Bernhard Schölkopf · Dominik Janzing
In this article 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 any different merging method that takes 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, with implications for Semi-Supervised Learning (SSL), and Out-Of-Variable (OOV) generalisation.
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