An Analysis of the Adaptation Speed of Causal Models
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 causeeffect 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 causeeffect 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/causaladaptationspeed
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2005.09136
 arXiv:
 arXiv:2005.09136
 Bibcode:
 2020arXiv200509136L
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Machine Learning
 EPrint:
 Published at AISTATS 2021. 10 pages main articles, 19 pages supplement, 10 figures