Upper Bound on Normalized Maximum Likelihood Codes for Gaussian Mixture Models

Understand

This paper shows that the normalized maximum likelihood~(NML) code-length calculated in [1] is an upper bound on the NML code-length strictly calculated for the Gaussian Mixture Model.

• When we use this upper bound on the NML code-length, we must change the scale of the data sequence to satisfy the restricted domain.
• However, we also show that the algorithm for model selection is essentially universal, regardless of the scale conversion of the data in Gaussian Mixture Models, and that, consequently, the experimental results in [1] can be used as they are.
• In addition to this, we correct the NML code-length in [1] for generalized logistic distributions.