A Stein-Papangelou Goodness-of-Fit Test for Point Processes
A Stein-Papangelou Goodness-of-Fit Test for Point Processes
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发表时间：
2019-04
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通讯作者：
Jiasen Yang;Vinayak A. Rao;Jennifer Neville
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作者：
Jiasen Yang;Vinayak A. Rao;Jennifer Neville
点过程提供了一个强大的框架，用于对事件在时间或空间中的分布和相互作用进行建模。它们的灵活性导致了统计和机器学习中各种复杂模型的出现，但模型诊断和批评技术仍然不发达。在这项工作中，我们提出了一个通用的Stein算子的基础上的Papangelou条件强度函数的点过程。然后，我们建立了一个核拟合优度测试通过定义一般点过程的Stein差异措施。值得注意的是，我们的测试也适用于非泊松点过程，其强度函数包含难以处理的归一化常数，由于点之间存在复杂的相互作用。我们应用我们提出的测试几个点过程模型，并表明它优于基于最大均值差异的双样本测试。
Point processes provide a powerful framework for modeling the distribution and interactions of events in time or space. Their flexibility has given rise to a variety of sophisticated models in statistics and machine learning, yet model diagnostic and criticism techniques remain underdeveloped. In this work, we propose a general Stein operator for point processes based on the Papangelou conditional intensity function. We then establish a kernel goodness-of-fit test by defining a Stein discrepancy measure for general point processes. Notably, our test also applies to non-Poisson point processes whose intensity functions contain intractable normalization constants due to the presence of complex interactions among points. We apply our proposed test to several point process models, and show that it outperforms a two-sample test based on the maximum mean discrepancy.