An Empirical Study of one of the Simplest Causal Prediction Algorithms

We study one of the simplest causal prediction algorithms that uses only conditional independences estimated from purely observational data. A specific pattern of four conditional independence relations amongst a quadruple of random variables already implies that one of these variables causes another one without any confounding. As a consequence, it is possible to predict what would happen under an intervention on that variable without actually performing the intervention. Although the method is asymptotically consistent and works well in settings with only few (latent) variables, we find that its prediction accuracy can be worse than simple (inconsistent) baselines when many (latent) variables are present. Our findings illustrate that violations of strong faithfulness become increasingly likely in the presence of many latent variables, and this can significantly deterioriate the accuracy of constraint-based causal prediction algorithms that assume faithfulness.