基于忠实性假设的k阶松弛的高阶马尔可夫毯发现
High-Order Markov Blanket Discovery via a k-Order Relaxation of the Faithfulness Assumption
浏览论文内容
中文总结 AI 辅助
该研究针对忠实性假设被高阶依赖等违反的问题，提出k阶松弛的忠实性假设，构建kOMB算法，实验证明其可在假设违反时恢复变量的马尔可夫毯
中文摘要 AI 辅助
从数据中学习变量的图马尔可夫毯（MB）的问题，在贝叶斯网络与马尔可夫随机场的结构学习、因果发现、特征选择等诸多领域都有应用。然而，大多数方法采用的常见假设是分布中的条件独立关系对应图结构中的相同分离，即忠实性假设。遗憾的是，该假设会被异或（XOR）、奇偶型关系等高阶依赖关系违反；在有限样本下，还会出现经验性违反，极端情况下甚至会引入真实分布中不存在的虚假依赖。因此，本文提出对忠实性假设进行“k阶”松弛，该松弛可捕获k+2个变量间的奇偶型关系。随后，我们提出一个概念验证算法，名为k阶马尔可夫毯（kOMB），该算法利用此松弛进行MB发现。最后，我们通过实验证明，在忠实性假设存在真实违反和经验违反的情况下，kOMB能够恢复变量的MB，代码可访问：this https URL
英文摘要
The problem of learning the graphical Markov blanket (MB) of a variable from data has applications in many areas such as structure learning for Bayesian networks and Markov random fields, causal discovery, and feature selection. However, a common assumption most methods make is that the conditional independencies in the distribution imply the same separation in the graphical structure -- also known as the faithfulness assumption. Unfortunately, this assumption can be violated by higher-order dependencies such as XOR and parity-type relations, and -- on finite samples -- by empirical violations that, in extreme cases, even induce spurious dependencies absent from the true distribution. Therefore, in this paper we propose a "k-order" relaxation of the faithfulness assumption that captures parity type relationships between k+2 variables. We then propose a proof of concept algorithm called k-order Markov blanket (kOMB) that uses this relaxation for MB discovery. Finally, we empirically show how kOMB can recover the MB of a variable under both true and empirical violations of faithfulness. Code available at: https://github.com/lklee9/k-order-Markov-blanket
发表机构
- Fraunhofer IAIS（弗劳恩霍夫智能分析与信息系统研究所）
- Hybrid Intelligence（混合智能机构）
机构由 AI 辅助整理，请以论文原文为准。
