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Statistics and Computing

, Volume 29, Issue 1, pp 161–176 | Cite as

Penalized estimation of directed acyclic graphs from discrete data

  • Jiaying Gu
  • Fei Fu
  • Qing ZhouEmail author
Article

Abstract

Bayesian networks, with structure given by a directed acyclic graph (DAG), are a popular class of graphical models. However, learning Bayesian networks from discrete or categorical data is particularly challenging, due to the large parameter space and the difficulty in searching for a sparse structure. In this article, we develop a maximum penalized likelihood method to tackle this problem. Instead of the commonly used multinomial distribution, we model the conditional distribution of a node given its parents by multi-logit regression, in which an edge is parameterized by a set of coefficient vectors with dummy variables encoding the levels of a node. To obtain a sparse DAG, a group norm penalty is employed, and a blockwise coordinate descent algorithm is developed to maximize the penalized likelihood subject to the acyclicity constraint of a DAG. When interventional data are available, our method constructs a causal network, in which a directed edge represents a causal relation. We apply our method to various simulated and real data sets. The results show that our method is very competitive, compared to many existing methods, in DAG estimation from both interventional and high-dimensional observational data.

Keywords

Coordinate descent Discrete Bayesian network Multi-logit regression Structure learning Group norm penalty 

Notes

Acknowledgements

This work was supported by NSF Grant IIS-1546098 (to Q.Z.).

Supplementary material

11222_2018_9801_MOESM1_ESM.pdf (249 kb)
Supplementary material 1 (pdf 248 KB)

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of CaliforniaLos AngelesUSA

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