从信息几何的角度重新审视依赖网络
Reconsidering Dependency Networks from an Information Geometry Perspective
摘要：
依赖网络（Heckerman等人，2000）是包括大量变量的系统的潜在概率图模型。与贝叶斯网络一样，依赖网络的结构由有向图表示，每个节点都有一个条件概率表。学习和推理是在单个节点上本地实现的;因此，即使有大量的变量，计算仍然是易于处理的。然而，依赖网络的学习分布是称为伪吉布斯采样的马尔可夫链的平稳分布，并且没有封闭形式的表达式。这一技术上的缺陷阻碍了依赖网络的发展。在本文中，我们考虑一个特定的流形为每个节点。然后，我们可以将伪吉布斯采样解释为这些流形上的迭代m投影。这种解释提供了一个理论界的位置，稳定分布的伪吉布斯抽样存在于分布空间。此外，这种解释涉及结构和参数学习算法作为优化问题。此外，我们比较依赖和贝叶斯网络的实验。结果表明，依赖网络和贝叶斯网络在学习分布的准确性方面具有大致相同的性能。结果还表明，依赖网络的学习速度比贝叶斯网络快得多。
英文摘要：
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph, and each node has a conditional probability table. Learning and inference are realized locally on individual nodes; therefore, computation remains tractable even with a large number of variables. However, the dependency network's learned distribution is the stationary distribution of a Markov chain called pseudo-Gibbs sampling and has no closed-form expressions. This technical disadvantage has impeded the development of dependency networks. In this paper, we consider a certain manifold for each node. Then, we can interpret pseudo-Gibbs sampling as iterative m-projections onto these manifolds. This interpretation provides a theoretical bound for the location where the stationary distribution of pseudo-Gibbs sampling exists in distribution space. Furthermore, this interpretation involves structure and parameter learning algorithms as optimization problems. In addition, we compare dependency and Bayesian networks experimentally. The results demonstrate that the dependency network and the Bayesian network have roughly the same performance in terms of the accuracy of their learned distributions. The results also show that the dependency network can learn much faster than the Bayesian network.
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