A fast score-based search algorithm for maximal ancestral graphs using entropy

Causal discovery is an essential part of causal inference (Spirtes et al., 2000; Peters et al., 2017), but estimating causal effects is extremely challenging if the underlying causal graph is unknown. Algorithms for learning causal graphs are many and varied, using different parametric structure, classes of graphical models, and assumptions about whether all relevant variables are measured (Spirtes et al., 2000; Kaltenpoth and Vreeken, 2023; Claassen and Bucur, 2022; Nowzohour et al., 2017; Zhang and Hyvarinen, 2009; Peters et al., 2017). In this paper, we consider only nonparametric assumptions, i.e. conditional independences in distributions that are represented by graphs. The primary graphical model used in causal inference is the directed acyclic graph, also known as a DAG. These offer a clear interpretation and are straightforward to conduct inference with, and are associated with probabilistic distributions by encoding conditional independence constraints.