A score-based approach is one that assigns a score that indicates how well a graph fits the data and then searches over the space of all the possible network structures to find a graph that maximizes the score. The score-based approaches enforce sparsity (fewer edges). This causes an optimization problem, where we have an exponential number of network structures to search over.
The likelihood score is a score that maximizes the likelihood of the data, given a particular graph structure G. The maximum likelihood estimates the parameters of G. Often, the log of the likelihood score is used. The likelihood score decomposes to the following formula:
The right-hand side of the equation consists of two terms: