Given a set of uncertain discrete variables with a joint probability distribution and a set of observations for some of them, the most probable explanation is a set or configuration of values for non-observed variables maximizing the conditional probability of these variables given the observations. This is a hard problem which can be solved by a deletion algorithm with max marginalization, having a complexity similar to the one of computing conditional probabilities. When this approach is unfeasible, an alternative is to carry out an approximate deletion algorithm, which can be used to guide the search of the most probable explanation, by using A* or branch and bound (the approximate+search approach). The most common approximation procedure has been the mini-bucket approach. In this paper it is shown that the use of probability trees as representation of potentials with a pruning of branches with similar values can improve the performance of this procedure. This is corroborated with an experimental study in which computation times are compared using randomly generated and benchmark Bayesian networks from UAI competitions.

中文翻译：

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使用 Mini-Bucket 和概率树逼近的贝叶斯网络中的 MPE 计算

给定一组具有联合概率分布的不确定离散变量以及其中一些变量的一组观测值，最可能的解释是一组或一组非观测变量的值，在给定观测值的情况下最大化这些变量的条件概率。这是一个难题，可以通过具有最大边缘化的删除算法来解决，其复杂性类似于计算条件概率的复杂性。当这种方法不可行时，一种替代方法是进行近似删除算法，该算法可用于指导搜索最可能的解释，通过使用 A*或分支定界（近似+搜索方法）。最常见的近似过程是迷你桶方法。在本文中，表明使用概率树来表示具有相似值的分支的修剪可以提高该过程的性能。一项实验研究证实了这一点，其中使用来自 UAI 比赛的随机生成和基准贝叶斯网络比较计算时间。