使用局部搜索近似MAP
Approximating MAP using Local Search
摘要：
MAP是在贝叶斯网络中找到一组变量的最可能实例的问题，给出证据。与计算边际、后验和MPE（MAP的一种特殊情况）不同，MAP的时间和空间复杂度不仅在网络树宽中呈指数级，而且在一个更大的参数（称为“约束”树宽）中也呈指数级。在实践中，这意味着计算MAP可能比计算后验或MPE贵几个数量级。因此，从业者一般避免MAP计算，而不是诉诸近似每个MAP variableseparately最可能的值，或MPE。我们提出了一种方法，近似MAP使用本地搜索。该方法的空间复杂度仅与树宽成指数关系，每步搜索的复杂度也是指数关系。我们研究了不同的局部搜索方法和几种初始化策略的有效性，并将它们与其他近似方案进行了比较.实验结果表明，局部搜索提供了一个更精确的近似MAP，同时需要很少的搜索步骤.实际上，这意味着局部搜索的复杂性往往只是在树宽上是指数级的，而不是在受限的树宽上，使得近似MAP与其他计算一样有效。
英文摘要：
MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network, given evidence. Unlike computing marginals, posteriors, and MPE (a special case of MAP), the time and space complexity of MAP is not only exponential in the network treewidth, but also in a larger parameter known as the "constrained" treewidth. In practice, this means that computing MAP can be orders of magnitude more expensive than computingposteriors or MPE. Thus, practitioners generally avoid MAP computations, resorting instead to approximating them by the most likely value for each MAP variableseparately, or by MPE.We present a method for approximating MAP using local search. This method has space complexity which is exponential onlyin the treewidth, as is the complexity of each search step. We investigate the effectiveness of different local searchmethods and several initialization strategies and compare them to otherapproximation schemes.Experimental results show that local search provides a much more accurate approximation of MAP, while requiring few search steps.Practically, this means that the complexity of local search is often exponential only in treewidth as opposed to the constrained treewidth, making approximating MAP as efficient as other computations.
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