# Quotient Normalized Maximum Likelihood Criterion for Learning Bayesian Network Structures

arXiv: https://arxiv.org/abs/2408.14935 · HTML: https://mlsanity.com/paper/2408.14935/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 33 references that are in the map.
- First posted on arXiv 27 Aug 2024.

## Builds on (most cited first, 5 of 5)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [A Transformational Characterization of Equivalent Bayesian Network Structures](https://mlsanity.com/paper/1302.4938/) (2013)
- [Theory Refinement on Bayesian Networks](https://mlsanity.com/paper/1303.5709/) (2013)
- [A Bayesian Approach to Learning Causal Networks](https://mlsanity.com/paper/1302.4958/) (2013)
- [A Theoretical Analysis of the BDeu Scores in Bayesian Network Structure Learning](https://mlsanity.com/paper/1607.04427/) (2016)

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

- [Conditional Density Estimation with Histogram Trees](https://mlsanity.com/paper/2410.11449/) (2024)

## Abstract (arXiv)

We introduce an information theoretic criterion for Bayesian network structure learning which we call quotient normalized maximum likelihood (qNML). In contrast to the closely related factorized normalized maximum likelihood criterion, qNML satisfies the property of score equivalence. It is also decomposable and completely free of adjustable hyperparameters. For practical computations, we identify a remarkably accurate approximation proposed earlier by Szpankowski and Weinberger. Experiments on both simulated and real data demonstrate that the new criterion leads to parsimonious models with good predictive accuracy.