In this chapter, we discuss information criteria (AIC and BIC) and Bayesian marginal likelihood, which play central roles in structure learning for graphical models. We first clarify the definitions and objectives of AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) and explain their positioning as selection methods based on the trade-off between goodness of fit and model complexity. Using linear regression models and categorical data as examples, we show how to compute these criteria concretely.