稀疏图模型熵的严密估计
Closely estimating the entropy of sparse graph models
摘要：
我们介绍了一种算法，用于估计成对的，概率图模型的熵，利用社会社区之间的桥梁和稀疏样本的准确熵估计。我们建议使用的投资措施，从社会学文献，伯特的结构约束，作为一种启发式的识别桥梁划分成有条件的独立组件的图形。我们结合这种启发式与Nemenman-Shafee-Bialek熵估计，以获得更快，更准确的估计。我们证明了它的成对最大熵，或伊辛，司法投票模型，以改善天真的熵估计。我们使用我们的算法来估计的配分函数密切，我们然后应用到模型选择的问题，估计的可能性是困难的。这是对依赖于点关联函数来测试拟合的现有方法的改进，可以通过对开源实现的直接修改来扩展到其他图模型。
英文摘要：
We introduce an algorithm for estimating the entropy of pairwise, probabilistic graph models by leveraging bridges between social communities and an accurate entropy estimator on sparse samples. We propose using a measure of investment from the sociological literature, Burt's structural constraint, as a heuristic for identifying bridges that partition a graph into conditionally independent components. We combine this heuristic with the Nemenman-Shafee-Bialek entropy estimator to obtain a faster and more accurate estimator. We demonstrate it on the pairwise maximum entropy, or Ising, models of judicial voting, to improve naïve entropy estimates. We use our algorithm to estimate the partition function closely, which we then apply to the problem of model selection, where estimating the likelihood is difficult. This serves as an improvement over existing methods that rely on point correlation functions to test fit can be extended to other graph models with a straightforward modification of the open-source implementation.
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