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Penalized estimation of directed acyclic graphs from discrete data

机译：来自离散数据的指向非循环图的惩罚估计

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摘要

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.
机译：贝叶斯网络，具有定向无循环图（DAG）给出的结构，是一种流行的图形模型。然而，由于大的参数空间和寻找稀疏结构的困难，从离散或分类数据学习来自离散或分类数据的贝叶斯网络尤其具有挑战性。在本文中，我们制定了最大的惩罚似然方法来解决这个问题。通过多记录回归，我们模拟了给定父项的节点的条件分布而不是常用的多项分布，其中边缘由一组系数矢量参数化，其中编码节点的级别的虚拟变量。为了获得稀疏的DAG，采用组规范惩罚，并且开发了一种群体坐标阶段算法以最大化受DAG的无循环性限制的惩罚可能性。当介入数据可用时，我们的方法构造了一个因果网络，其中定向边缘表示因果关系。我们将方法应用于各种模拟和实际数据集。结果表明，与许多现有方法相比，我们的方法非常有竞争力，在介入和高维观察数据中的DAG估计中。

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