基于与贝叶斯非参数混合模型联系的Neyman-Scott过程时空聚类
Spatiotemporal Clustering with Neyman-Scott Processes via Connections to Bayesian Nonparametric Mixture Models
AI总结：
本文揭示了Neyman-Scott过程与Dirichlet过程混合模型通过有限混合模型建立的新联系，借此改编坍缩吉布斯采样算法实现可扩展贝叶斯推断，并验证了其在神经脉冲序列与文档流等时空数据聚类任务中的有效性。
摘要：
Neyman-Scott过程（NSP）是在时间或空间中生成点簇的点过程模型。它们是涵盖从神经脉冲序列到文档流等广泛现象的自然模型。其聚类特性通过双重随机公式实现：首先，从泊松过程中提取一组潜在事件；然后，每个潜在事件根据另一个泊松过程生成一组观测数据点。这种构造类似于Dirichlet过程混合模型（DPMM）等贝叶斯非参数混合模型，因为潜在事件（即簇）的数量是随机变量，但点过程公式使NSP特别适合于对时空数据进行建模。尽管已为DPMM开发了许多专门的算法，但相比之下，关注NSP推断的研究较少。在此，我们提出了NSP与DPMM之间的新联系，其关键纽带是被称为有限混合模型混合（MFMM）的第三类贝叶斯混合模型。利用这一联系，我们将DPMM的标准坍缩吉布斯采样算法进行调整，以实现对NSP模型的可扩展贝叶斯推断。我们展示了Neyman-Scott过程在多种应用中的潜力，包括神经脉冲序列中的序列检测和文档流中的事件检测。
英文摘要：
Neyman-Scott processes (NSPs) are point process models that generate clusters of points in time or space. They are natural models for a wide range of phenomena, ranging from neural spike trains to document streams. The clustering property is achieved via a doubly stochastic formulation: first, a set of latent events is drawn from a Poisson process; then, each latent event generates a set of observed data points according to another Poisson process. This construction is similar to Bayesian nonparametric mixture models like the Dirichlet process mixture model (DPMM) in that the number of latent events (i.e. clusters) is a random variable, but the point process formulation makes the NSP especially well suited to modeling spatiotemporal data. While many specialized algorithms have been developed for DPMMs, comparatively fewer works have focused on inference in NSPs. Here, we present novel connections between NSPs and DPMMs, with the key link being a third class of Bayesian mixture models called mixture of finite mixture models (MFMMs). Leveraging this connection, we adapt the standard collapsed Gibbs sampling algorithm for DPMMs to enable scalable Bayesian inference on NSP models. We demonstrate the potential of Neyman-Scott processes on a variety of applications including sequence detection in neural spike trains and event detection in document streams.
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