An Analysis of the Adaptation Speed of Causal Models
This work addresses the problem of model selection in causal inference for researchers, providing theoretical insights that challenge existing conjectures, though it is incremental in refining prior experimental findings.
The paper analyzes the adaptation speed of causal models to interventions, showing that the correct causal direction is significantly faster when the cause is intervened on, but surprisingly, the anticausal model can be faster when the effect is intervened on, falsifying a prior hypothesis.
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