The Lauritzen-Chen Likelihood For Graphical Models
图模型的 Lauritzen–Chen 似然AI 解读 ↓
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图模型的 Lauritzen–Chen 似然
- 研究问题
- 如何为一般参数与半参数图模型构造兼容且无冗余的似然，并避免同一马尔可夫等价类中的不同有向图引入额外边方向假设？
- 方法与思路
- 作者连接 Chen 的密度分解与 Lauritzen 的团分解，构造无向图模型似然，再扩展到有向无环图，使同一马尔可夫等价类共享似然。
- 材料陈述的贡献
- 摘要称，该似然由变分独立、无冗余的观测分布闭式泛函组成，适用于一般参数和半参数模型，并可用于模型选择及半参数推断。
- 阅读关注点
- 应核对闭式泛函与变分独立的具体定义、参数空间兼容条件，以及有向图扩展如何保证等价类内一致；还需检查实际拟合与选择程序。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实。摘要未给出具体构造、适用条件或计算表现，等价类内似然一致也不意味着能识别真实边方向。
原文摘要
Graphical models such as Markov random fields (MRFs) that are associated with undirected graphs, and Bayesian networks (BNs) that are associated with directed acyclic graphs, have proven to be a very popular approach for reasoning under uncertainty, prediction problems and causal inference. Parametric MRF likelihoods are well-studied for Gaussian and categorical data. However, in more complicated parametric and semi-parametric settings, likelihoods specified via clique potential functions are generally not known to be congenial {(jointly well-specified)} or non-redundant. Congenial and non-redundant DAG likelihoods are far simpler to specify in both parametric and semi-parametric settings by modeling Markov factors in the DAG factorization. However, DAG likelihoods specified in this way are not guaranteed to coincide in distinct DAGs within the same Markov equivalence class. This complicates likelihoods based model selection procedures for DAGs by ``sneaking in'' potentially unwarranted assumptions about edge orientations. In this paper we link a density function decomposition due to Chen with the clique factorization of MRFs described by Lauritzen to provide a general likelihood for MRF models. The proposed likelihood is composed of variationally independent, and non-redundant closed form functionals of the observed data distribution, and is sufficiently general to apply to arbitrary parametric and semi-parametric models. We use an extension of our developments to give a general likelihood for DAG models that is guaranteed to coincide for all members of a Markov equivalence class. Our results have direct applications for model selection and semi-parametric inference.