# Moment-Matching Conditions for Exponential Families with Conditioning or Hidden Data

arXiv: https://arxiv.org/abs/2001.09771 · HTML: https://mlsanity.com/paper/2001.09771/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [The Well-Tempered Classifier: Some Elementary Properties of Temperature Scaling](https://mlsanity.com/paper/2602.14862/) (2026)

## Abstract (arXiv)

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.