# Learning complex dependency structure of gene regulatory networks from high dimensional micro-array data with Gaussian Bayesian networks

arXiv: https://arxiv.org/abs/2106.15365 · HTML: https://mlsanity.com/paper/2106.15365/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 47 references that are in the map.
- First posted on arXiv 28 Jun 2021.

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

- [Concave Penalized Estimation of Sparse Gaussian Bayesian Networks](https://mlsanity.com/paper/1401.0852/) (2014)
- [A Tutorial on Regularized Partial Correlation Networks](https://mlsanity.com/paper/1607.01367/) (2016)
- [Learning Large-Scale Bayesian Networks with the sparsebn Package](https://mlsanity.com/paper/1703.04025/) (2017)
- [Learning Graphical Models With Hubs](https://mlsanity.com/paper/1402.7349/) (2014)
- [The Probabilistic Backbone of Data-Driven Complex Networks: An example in Climate](https://mlsanity.com/paper/1912.03758/) (2019)

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

- [The Impact of Variable Ordering on Bayesian Network Structure Learning](https://mlsanity.com/paper/2206.08952/) (2022)

## Abstract (arXiv)

Gene expression datasets consist of thousand of genes with relatively small samplesizes (i.e. are large-p-small-n). Moreover, dependencies of various orders co-exist in the datasets. In the Undirected probabilistic Graphical Model (UGM) framework the Glasso algorithm has been proposed to deal with high dimensional micro-array datasets forcing sparsity. Also, modifications of the default Glasso algorithm are developed to overcome the problem of complex interaction structure. In this work we advocate the use of a simple score-based Hill Climbing algorithm (HC) that learns Gaussian Bayesian Networks (BNs) leaning on Directed Acyclic Graphs (DAGs). We compare HC with Glasso and its modifications in the UGM framework on their capability to reconstruct GRNs from micro-array data belonging to the Escherichia Coli genome. We benefit from the analytical properties of the Joint Probability Density (JPD) function on which both directed and undirected PGMs build to convert DAGs to UGMs. We conclude that dependencies in complex data are learned best by the HC algorithm, presenting them most accurately and efficiently, simultaneously modelling strong local and weaker but significant global connections coexisting in the gene expression dataset. The HC algorithm adapts intrinsically to the complex dependency structure of the dataset, without forcing a specific structure in advance. On the contrary, Glasso and modifications model unnecessary dependencies at the expense of the probabilistic information in the network and of a structural bias in the JPD function that can only be relieved including many parameters.