# Does information criteria (AIC, BIC and DIC...) imply "causality"?

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.

e.g., causal-learn

"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) [2]." from a Medium article

• They don't. They are purely statistical measures of association. (Which of course does not preclude using them in a screening step in a causal analysis.) That at least is my understanding, maybe someone has found a way to interpret ICs causally... I would be interested in learning something new here. Commented Jul 12, 2023 at 14:09
• As @StephanKolassa said. The various IC s are methods for fitting the best model. If it's also causal, then ... they pick good causal models. Commented Jul 12, 2023 at 14:25
• I will be brutally honest here: most Python libraries are written by computer scientists or software engineers, and that is usually a Good Thing. However, no matter how many "Machine Learning" courses they have taken (or published), they are not statisticians, and most do not display a deep understanding of statistics or the difference between statistical association and information criteria. There, I've said it. Commented Jul 12, 2023 at 15:41
• I agree with the other comments - no causality is proven. For causality, you really need a causal diagram / model. There's a great book "They Book of Why" which discusses several examples - how using tar in the lungs (if I recall correctly) as a mediator for the effect of smoking on lung cancer disproved the common cause hypothesis. Commented Jul 12, 2023 at 15:49
• Lots of great comments here. The idea that causality can be learned solely from data is laughable. Commented Jul 12, 2023 at 16:04