Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks
Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks
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DOI：
10.1023/a:1020249912095
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发表时间：
2003-01-01
期刊：
影响因子：
7.5
通讯作者：
Koller, D
中科院分区：
文献类型：
--
作者：
Friedman, N;Koller, D
在许多多变量域中，我们对分析底层分布的依赖结构感兴趣，例如，两个变量是否直接相互作用。我们可以使用贝叶斯网络模型来表示依赖结构。为了分析给定的数据集，贝叶斯模型选择试图找到最可能的（MAP）模型，并使用其结构来回答这些问题。然而，当可用数据量适中时，可能有许多模型具有不可忽略的后验。因此，我们想要计算特征的贝叶斯后验，即，包含它的所有模型的总后验概率。在本文中，我们提出了一种新的方法来完成这项任务。我们首先展示了如何有效地计算网络变量与固定顺序一致的指数网络的总和。这使我们能够计算，对于给定的顺序，数据的边缘概率和后验特征。然后，我们使用这个结果作为一个算法的基础，近似贝叶斯后验的功能。我们的方法使用马尔可夫链蒙特卡罗（MCMC）方法，但订单，而不是网络结构。序空间比结构空间更小更规则，并且具有更平滑的后“景观”。我们在合成和现实生活中的数据集上提出了实证结果，将我们的方法与完整模型平均（如果可能），网络结构上的MCMC以及非贝叶斯自助方法进行了比较。
In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior "landscape". We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.