In recent years the possibility of relaxing the so-called Faithfulness
assumption in automated causal discovery has been investigated. The
investigation showed (1) that the Faithfulness assumption can be weakened in
various ways that in an important sense preserve its power, and (2) that
weakening of Faithfulness may help to speed up methods based on Answer Set
Programming. However, this line of work has so far only considered the
discovery of causal models without latent variables. In this paper, we study
weakenings of Faithfulness for constraint-based discovery of semi-Markovian
causal models, which accommodate the possibility of latent variables, and show
that both (1) and (2) remain the case in this more realistic setting.

研究了自动因果发现中所谓的忠实性假设的可能性和弱化，发现可以在重要意义上保留其功能的各种方式，并且弱化忠实性可以帮助加速基于答案集编程的方法。此外，本文还探讨了半马尔可夫因果模型的基于约束的发现中忠实性的弱化，发现在这种更现实的情况下保持了（1）和（2）的情况，并考虑到了潜变量的可能性。

基于 ASP 的半马尔科夫因果模型发现算法在较弱假设下的应用

ASP-based Discovery of Semi-Markovian Causal Models under Weaker  Assumptions

Many algorithms for inferring causality rely heavily on the faithfulness
assumption. The main justification for imposing this assumption is that the set
of unfaithful distributions has Lebesgue measure zero, since it can be seen as
a collection of hypersurfaces in a hypercube. However, due to sampling error
the faithfulness condition alone is not sufficient for statistical estimation,
and strong-faithfulness has been proposed and assumed to achieve uniform or
high-dimensional consistency. In contrast to the plain faithfulness assumption,
the set of distributions that is not strong-faithful has nonzero Lebesgue
measure and in fact, can be surprisingly large as we show in this paper. We
study the strong-faithfulness condition from a geometric and combinatorial
point of view and give upper and lower bounds on the Lebesgue measure of
strong-faithful distributions for various classes of directed acyclic graphs.
Our results imply fundamental limitations for the PC-algorithm and potentially
also for other algorithms based on partial correlation testing in the Gaussian
case.

该论文研究了因果推断中的忠诚度假设及其限制，探究了在不同有向无环图的情况下强忠诚度分布的上下界，并证明了忠诚度假设对于 PC 算法以及高斯偏相关测试等算法具有基本的限制。