We consider the problem of discovering the causal process that generated a collection of datasets. We assume that all these datasets were generated by unknown sparse interventions on a structural causal model (SCM) $G$, that we want to identify. Recently, Bengio et al. (2020) argued that among all SCMs, $G$ is the fastest to adapt from one dataset to another, and proposed a meta-learning criterion to identify the causal direction in a two-variable SCM. While the experiments were promising, the theoretical justification was incomplete. Our contribution is a theoretical investigation of the adaptation speed of simple two-variable SCMs. We use convergence rates from stochastic optimization to justify that a relevant proxy for adaptation speed is distance in parameter space after intervention. Using this proxy, we show that the SCM with the correct causal direction is advantaged for categorical and normal cause-effect datasets when the intervention is on the cause variable. When the intervention is on the effect variable, we provide a more nuanced picture which highlights that the fastest-to-adapt heuristic is not always valid. Code to reproduce experiments is available at https://github.com/remilepriol/causal-adaptation-speed

本文在未知的结构因果模型G执行未知干预收集的数据集的基础上，使用随机优化的收敛速率，对因果关系下的结构因果模型(SCMs)适应速度进行了研究，并利用参数空间距离作为代理来衡量适应速度。我们发现，当干预在原因变量上时，SCM的正确因果方向会得到巨大优势，而当干预在效应变量上时，我们对其相对适应速度进行了表征。令人惊讶的是，我们发现反因果模型在某些情况下具有优势，从而推翻初始假设。

因果模型适应速度分析