MixtureICLBICCriterion

The integrated completed likelihood, in its approximation by the Bayesian information criterion penalized by the classification entropy.

This is the criterion matched to a classification-based fitting method: the entropy term penalizes a mixture whose components overlap, so it selects for a partition that classifies the data cleanly rather than merely fitting its density. The responsibilities it needs are computed from the same candidate.

The name reflects what is computed. This is not the exact integrated completed likelihood but its information-criterion approximation, and the distinction matters when comparing against published results.