We consider the problem of lower bounding the error probability under the invariant causal prediction (ICP) framework. To this end, we examine and draw connections between ICP and the zero-rate Gaussian multiple access channel by first proposing a variant of the original invariant prediction assumption, and then considering a special case of the Gaussian multiple access channel where a codebook is shared between an unknown number of senders. This connection allows us to develop three types of lower bounds on the error probability, each with different assumptions and constraints, leveraging techniques for multiple access channels. The proposed bounds are evaluated with respect to existing causal discovery methods as well as a proposed heuristic method based on minimum distance decoding.

翻译：我们考虑在不变因果预测（ICP）框架下对错误概率进行下界估计的问题。为此，我们首先通过提出原始不变预测假设的一个变体，并考虑高斯多址信道中一个未知数量发送者共享码本的特殊情形，来探究ICP与零速率高斯多址信道之间的关联。这种关联使我们能够利用多址信道技术，在三种不同假设与约束条件下分别推导出错误概率的下界。我们将所提出的界与现有因果发现方法以及基于最小距离解码的启发式方法进行了对比评估。