I am interested in finding out the graphical causal structure. Causal Discovery algorithms (e.g., DAG learning) are used to identify potential causal graphs. In score-based causal discovery methods, many model scores such as AIC, BIC, and DIC have been utilized to compare models and to pick up the best "causal" graph. For example, Greedy Search Algorithm tries to find the minimal BIC's graph as a potential causal graph.
But, I am still not sure about how they can use such scores for "causality"-based model comparison. I know that such scores may represent the better "goodness of fit" but I cannot find out some materials that such scores may represent "causal relationships". Could you help me to understand why such scores can imply causal structures?
There are a lot of causal discovery / DAG learning packages to use such ICs to find out causal graphs.
"The Greedy Equivalence Search (GES) algorithm uses this trick. GES starts with an empty graph and iteratively adds directed edges such that the improvement in a model fitness measure (i.e. score) is maximized. An example score is the Bayesian Information Criterion (BIC) ." from a Medium article