从信息几何角度重新分析依赖网络采样机制，揭示其分布收敛性。
Reconsidering Dependency Networks from an Information Geometry Perspective
- 将伪吉布斯采样视为m-投影，构建全条件流形上的几何解释
- 导出全条件散度上界，证明模型分布随样本数无限增长而收敛于真分布
- 适用于需理论保障的复杂系统建模，适合概率图模型研究者
依赖网络（Heckerman et al., 2000）通过独立学习局部条件分布并结合伪吉布斯采样，为多变量复杂系统建模提供灵活框架。尽管计算效率优于贝叶斯与马尔可夫网络，其理论基础仍不完整，因模型分布（定义为伪吉布斯采样的平稳分布）缺乏闭式表达。本文从信息几何视角分析伪吉布斯采样，将每一步采样解释为对全条件流形的m-投影。基于此，引入全条件散度，并推导出描述平稳分布位置的上界。进一步将结构与参数学习重构为可分解为各节点独立子问题的优化问题，并证明当训练样本数趋于无穷时，学习到的模型分布收敛至真实分布。实验验证该上界在实践中具有紧性。
原文摘要 · Abstract (English)
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their computational advantages over Bayesian and Markov networks, the theoretical foundations of dependency networks remain incomplete, primarily because their model distributions -- defined as stationary distributions of pseudo-Gibbs sampling -- lack closed-form expressions. This paper develops an information-geometric analysis of pseudo-Gibbs sampling, interpreting each sampling step as an m-projection onto a full conditional manifold. Building on this interpretation, we introduce the full conditional divergence and derive an upper bound that characterizes the location of the stationary distribution in the space of probability distributions. We then reformulate both structure and parameter learning as optimization problems that decompose into independent subproblems for each node, and prove that the learned model distribution converges to the true underlying distribution as the number of training samples grows to infinity. Experiments confirm that the proposed upper bound is tight in practice.
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