通过与贝叶斯非参数混合模型的连接,使用Neyman-Scott过程进行时空聚类
Yixin Wang1, Anthony Degleris2, Alex Williams3,4
1Department of Statistics, University of Michigan, Ann Arbor, MI, USA.
Journal of the American Statistical Association
|September 23, 2024
概括
尼曼-斯科特过程 (NSP) 模拟集群数据,如神经或文档. 我们将NSP与混合模型联系起来,使得可扩展的贝叶斯推理能够更好地进行时空数据分析.
科学领域:
- 计算统计学 计算统计学
- 点流程建模点流程建模
- 贝叶斯的推理是贝叶斯的推理.
背景情况:
- 尼曼-斯科特过程 (NSP) 是点过程模型,能够在时间或空间中捕获集群数据.
- 它们的双重随机配方,涉及潜在事件产生观察到的点,使它们适合神经尖峰列车和文档流等现象.
- 尽管它们具有实用性,但与类似的贝叶斯非参数混合模型相比,NSP的专用推理算法较不发达.
研究的目的:
- 在尼曼-斯科特过程 (NSP) 和贝叶斯混合模型之间建立新的连接,特别是迪里克莱特过程混合模型 (DPMMs) 和有限混合模型 (MFMMs) 的混合.
- 为DPMM适应现有的推理算法,以便为NSP模型提供可扩展的贝叶斯推理.
- 在现实世界时空数据集上展示增强的NSP推断方法的实际应用性.
主要方法:
- 建立尼曼-斯科特过程 (NSP) 和混合有限混合模型 (MFMMs) 之间的理论联系.
- 适应通常用于DPMM的崩的吉布斯采样算法,以在NSP中进行高效的推理.
- 应用开发的推理框架来分析神经尖端列车中的序列检测和文档流中的事件检测.
主要成果:
- 在NSP和MFMM之间确定了一个关键的联系,为推断提供了一个桥梁.
- 适应的吉布斯抽样算法使NSP模型能够进行可扩展的贝叶斯推理.
- 该方法的成功应用证明了其在复杂的时空数据中对序列和事件检测的潜力.
结论:
- 建立的连接和适应的推理算法显著提高了Neyman-Scott过程的分析能力.
- 针对NSP的可扩展贝叶斯推理为复杂的聚类时空数据建模开辟了新的途径.
- 展示的应用突显了NSP在神经科学和文本分析等领域的实际价值.
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