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An Analysis of the Adaptation Speed of Causal Models

Remi Le Priol · Reza Babanezhad · Yoshua Bengio · Simon Lacoste-Julien

Keywords: [ Deep Learning ] [ Generative Models ] [ Algorithms -> Unsupervised Learning; Applications -> Computer Vision; Deep Learning ] [ Adversarial Networks ] [ Learning Theory and Statistics ] [ Causality ]

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.

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