# Testing Sparsity Assumptions in Bayesian Networks

arXiv: https://arxiv.org/abs/2307.06406 · HTML: https://mlsanity.com/paper/2307.06406/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 32 references that are in the map.
- First posted on arXiv 12 Jul 2023.

## Builds on (most cited first, 3 of 3)

- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator](https://mlsanity.com/paper/1805.07194/) (2018)
- [Nonparametric Stein-type Shrinkage Covariance Matrix Estimators in High-Dimensional Settings](https://mlsanity.com/paper/1410.4726/) (2014)

## Abstract (arXiv)

Bayesian network (BN) structure discovery algorithms typically either make assumptions about the sparsity of the true underlying network, or are limited by computational constraints to networks with a small number of variables. While these sparsity assumptions can take various forms, frequently the assumptions focus on an upper bound for the maximum in-degree of the underlying graph nablaG. Theorem 2 in Duttweiler et. al. (2023) demonstrates that the largest eigenvalue of the normalized inverse covariance matrix (Omega) of a linear BN is a lower bound for nablaG. Building on this result, this paper provides the asymptotic properties of, and a debiasing procedure for, the sample eigenvalues of Omega, leading to a hypothesis test that may be used to determine if the BN has max in-degree greater than 1. A linear BN structure discovery workflow is suggested in which the investigator uses this hypothesis test to aid in selecting an appropriate structure discovery algorithm. The hypothesis test performance is evaluated through simulations and the workflow is demonstrated on data from a human psoriasis study.