# Causal vs. Anticausal merging of predictors

arXiv: https://arxiv.org/abs/2501.08426 · HTML: https://mlsanity.com/paper/2501.08426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 14 Jan 2025.

## Builds on (most cited first, 6 of 6)

- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [Causal Direction of Data Collection Matters: Implications of Causal and Anticausal Learning for NLP](https://mlsanity.com/paper/2110.03618/) (2021)
- [Fisher and Kernel Fisher Discriminant Analysis: Tutorial](https://mlsanity.com/paper/1906.09436/) (2019)
- [Causal versions of Maximum Entropy and Principle of Insufficient Reason](https://mlsanity.com/paper/2102.03906/) (2021)
- [Causal and anti-causal learning in pattern recognition for neuroimaging](https://mlsanity.com/paper/1512.04808/) (2015)
- [Out-of-Variable Generalization for Discriminative Models](https://mlsanity.com/paper/2304.07896/) (2023)

## Built on by (most cited first, 1 of 1)

- [Measure-Theoretic Anti-Causal Representation Learning](https://mlsanity.com/paper/2510.18052/) (2025)

## Abstract (arXiv)

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.