Moment-Matching Conditions for Exponential Families with Conditioning or Hidden Data
This work offers theoretical clarification for statistical learning problems involving conditioning or incomplete data, but it is incremental as it builds on classic exponential family results.
The paper tackles the generalization of maximum likelihood learning's moment-matching conditions to conditional exponential families and hidden data scenarios, providing a first-principles explanation and derivation.
Maximum likelihood learning with exponential families leads to moment-matching of the sufficient statistics, a classic result. This can be generalized to conditional exponential families and/or when there are hidden data. This document gives a first-principles explanation of these generalized moment-matching conditions, along with a self-contained derivation.