An Analysis of the Adaptation Speed of Causal Models

TL;DR

This paper analyzes the adaptation speed of causal models after interventions, providing theoretical justifications and empirical results that challenge previous assumptions about causal direction advantages.

Contribution

It offers a thorough analysis of the adaptation speed of cause-effect SCMs, including new theoretical insights and empirical evaluations that reveal surprising cases.

Findings

Causal models adapt faster when intervening on the cause variable.

The correct causal direction often leads to faster adaptation.

In some cases, anticausal models adapt faster, contradicting initial hypotheses.

Abstract

Consider a collection of datasets generated by unknown interventions on an unknown structural causal model $G$. Recently, Bengio et al. (2020) conjectured that among all candidate models, $G$ is the fastest to adapt from one dataset to another, along with promising experiments. Indeed, intuitively $G$ has less mechanisms to adapt, but this justification is incomplete. Our contribution is a more thorough analysis of this hypothesis. We investigate the adaptation speed of cause-effect SCMs. Using convergence rates from stochastic optimization, we justify that a relevant proxy for adaptation speed is distance in parameter space after intervention. Applying this proxy to categorical and normal cause-effect models, we show two results. When the intervention is on the cause variable, the SCM with the correct causal direction is advantaged by a large factor. When the intervention is on the effect variable, we characterize the relative adaptation speed. Surprisingly, we find situations where the anticausal model is advantaged, falsifying the initial hypothesis. Code to reproduce experiments is available at https://github.com/remilepriol/causal-adaptation-speed