驯服离散性的诅咒：通过散列和优化的离散积分
Taming the Curse of Dimensionality: Discrete Integration by Hashing and Optimization
摘要：
集成受到维数灾难的影响，并且随着问题维数的增加而迅速变得难以处理。我们提出了一个随机算法，具有很高的概率，给出了一个常数因子近似的一般离散积分定义在一个指数大的集合。该算法仅依赖于解决离散组合优化问题的少量实例，该问题受到用作散列函数的随机生成的奇偶校验约束。作为一个应用程序，我们证明了少量的MAP查询，我们可以有效地近似离散图形模型，这反过来又可以用于，例如，边际计算或模型选择的分区函数。
英文摘要：
Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a general discrete integral defined over an exponentially large set. This algorithm relies on solving only a small number of instances of a discrete combinatorial optimization problem subject to randomly generated parity constraints used as a hash function. As an application, we demonstrate that with a small number of MAP queries we can efficiently approximate the partition function of discrete graphical models, which can in turn be used, for instance, for marginal computation or model selection.
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