退火MAP
Annealed MAP
摘要：
最大后验分配（MAP）是在贝叶斯网络中，在给定其他变量的部分证据的情况下，找到一组变量的最可能实例的问题。MAP已被证明是一个NP难问题[22]，即使是对于约束网络，如polytree [18]。因此，以前的方法往往无法产生任何结果的MAP问题在大型复杂的贝叶斯网络。为了解决这个问题，我们提出了AnnealedMAP算法，一种基于模拟退火的MAP算法。AnnealedMAP算法模拟了一个非齐次马尔可夫链，其不变函数是一个概率密度，集中在目标密度的模式。我们在几个真实的贝叶斯网络上测试了该算法。结果表明，在保持良好质量的MAP解决方案，退火MAP算法也能够解决许多问题，是以前的方法无法达到的。
英文摘要：
Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22], even for constrained networks, such as polytrees [18]. Hence, previous approaches often fail to yield any results for MAP problems in large complex Bayesian networks. To address this problem, we propose AnnealedMAP algorithm, a simulated annealing-based MAP algorithm. The AnnealedMAP algorithm simulates a non-homogeneous Markov chain whose invariant function is a probability density that concentrates itself on the modes of the target density. We tested this algorithm on several real Bayesian networks. The results show that, while maintaining good quality of the MAP solutions, the AnnealedMAP algorithm is also able to solve many problems that are beyond the reach of previous approaches.
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