最大熵下的Credal网络
Credal Networks under Maximum Entropy
摘要：
我们应用最大熵原理从一个可信网络指定的所有联合概率分布集中选择一个唯一的联合概率分布。详细地说，我们首先证明贝叶斯树的唯一联合分布与其条件分布的最大熵模型相吻合。然而，这一结果不再适用于一般的贝叶斯网络。因此，我们提出了一种新的最大熵模型，这是连续计算。然后，我们表明，对于所有一般的贝叶斯网络，序列最大熵模型符合唯一的联合分布。此外，我们将新的顺序最大熵原理应用于区间贝叶斯网络和更一般的信用网络。我们特别表明，这个应用程序是相当于一些小的局部熵最大化。
英文摘要：
We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy model of its conditional distributions. This result, however, does not hold anymore for general Bayesian networks. We thus present a new kind of maximum entropy models, which are computed sequentially. We then show that for all general Bayesian networks, the sequential maximum entropy model coincides with the unique joint distribution. Moreover, we apply the new principle of sequential maximum entropy to interval Bayesian networks and more generally to credal networks. We especially show that this application is equivalent to a number of small local entropy maximizations.
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