Mixture Conjugation Utilities

Mixture model utilities for conjugated harmoniums.

This module provides helper functions for computing conjugation parameters in hierarchical mixture models, enabling efficient inference in models where conjugated harmoniums are composed into mixture structures.

Key function: harmonium_mixture_conjugation_parameters decomposes the joint conjugation parameters of a mixture of conjugated harmoniums into three components:

1. Y conjugation biases: Base conjugation parameters from the first component

2. K conjugation biases: Differences in log partition between components

3. K-Y interaction: Changes in conjugation parameters across components

This decomposition preserves the mixture structure and enables efficient conjugation parameter computation for hierarchical models where the upper level is a mixture over harmoniums.