A Critical View of the Structural Causal Model

DSA ADS Course - 2021

Causal Inference, Causality, Structural Causal Model, SCM

Discuss causality vs. correlation - causality vs. statistics in machine learning. Review techniques for attempting to find true causality. 

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. In the broadest sense correlation is any statistical association, though it commonly refers to the degree to which a pair of variables are linearly related.

Discuss causal inference using Structural Causal Model (SCM) along with downside risks. What is relationship between cause and effect? Risk of reversing cause and effect. Causality concerns relationships where a change in one variable necessarily results in a change in another variable. There are three conditions for causality: covariation, temporal precedence, and control for “third variables.” The latter comprise alternative explanations for the observed causal relationship.

A Critical View of the Structural Causal Model - February, 2020

Abstract

In the univariate case, we show that by comparing the individual complexities of univariate cause and effect, one can identify the cause and the effect, without considering their interaction at all. In our framework, complexities are captured by the reconstruction error of an autoencoder that operates on the quantiles of the distribution. Comparing the reconstruction errors of the two autoencoders, one for each variable, is shown to perform surprisingly well on the accepted causality directionality benchmarks.

Hence, the decision as to which of the two is the cause and which is the effect may not be based on causality but on complexity. In the multivariate case, where one can ensure that the complexities of the cause and effect are balanced, we propose a new adversarial training method that mimics the disentangled structure of the causal model.

We prove that in the multidimensional case, such modeling is likely to fit the data only in the direction of causality. Furthermore, a uniqueness result shows that the learned model is able to identify the underlying causal and residual (noise) components. Our multidimensional method outperforms the literature methods on both synthetic and real world datasets.