一种基于熵的快速分数搜索算法用于极大祖先图
A fast score-based search algorithm for maximal ancestral graphs using entropy
AI总结：
提出一种基于熵和细化马尔可夫性质的分数搜索算法，通过限制度、头部大小和判别路径实现多项式复杂度，在模拟实验中优于现有MAG学习方法。
摘要：
极大祖先图（MAGs）是一类图形模型，在存在潜在混杂因素的情况下扩展了著名的有向无环图。大多数基于分数的方法从经验数据中学习未知的MAG时依赖于BIC分数，而BIC分数存在不稳定和计算量大的问题。我们提出使用imsets框架，通过经验熵估计和新提出的细化马尔可夫性质来对MAG进行评分。我们的图形搜索过程类似于claassen2022greedy，但根据我们的理论结果进行了改进。我们证明，通过限制度、最大头部大小和判别路径的数量，我们的搜索算法在节点数量上是多项式的。在模拟实验中，我们的算法显示出优于其他最先进的MAG学习算法的性能。
英文摘要：
\emph{Maximal ancestral graph} (MAGs) is a class of graphical model that extend the famous \emph{directed acyclic graph} in the presence of latent confounders. Most score-based approaches to learn the unknown MAG from empirical data rely on BIC score which suffers from instability and heavy computations. We propose to use the framework of imsets \citep{studeny2006probabilistic} to score MAGs using empirical entropy estimation and the newly proposed \emph{refined Markov property} \citep{hu2023towards}. Our graphical search procedure is similar to \citet{claassen2022greedy} but improved from our theoretical results. We show that our search algorithm is polynomial in number of nodes by restricting degree, maximal head size and number of discriminating paths. In simulated experiment, our algorithm shows superior performance compared to other state of art MAG learning algorithms.
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