# Hierarchical Multinomial-Dirichlet model for the estimation of conditional probability tables

arXiv: https://arxiv.org/abs/1708.06935 · HTML: https://mlsanity.com/paper/1708.06935/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2017.

## Built on by (most cited first, 2 of 2)

- [A first approach to closeness distributions](https://mlsanity.com/paper/2111.08357/) (2021)
- [Learning discrete Bayesian networks with hierarchical Dirichlet shrinkage](https://mlsanity.com/paper/2509.13267/) (2025)

## Abstract (arXiv)

We present a novel approach for estimating conditional probability tables, based on a joint, rather than independent, estimate of the conditional distributions belonging to the same table. We derive exact analytical expressions for the estimators and we analyse their properties both analytically and via simulation. We then apply this method to the estimation of parameters in a Bayesian network. Given the structure of the network, the proposed approach better estimates the joint distribution and significantly improves the classification performance with respect to traditional approaches.