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多元高斯图模型及其在多元格子数据中的应用
Multi-way Gaussian Graphical Models with Application to Multivariate Lattice Data |
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| 课程网址: |
http://videolectures.net/aistats2011_dobra_application/
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| 主讲教师: |
Adrian Dobra
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| 开课单位: |
华盛顿大学
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| 开课时间: |
2011-05-06
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| 课程语种: |
英语
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| 中文简介: |
关于高斯图形模型(GGMs)的文献包含了两个同样丰富和同样重要的研究领域和兴趣。第一个研究领域涉及图的确定问题。也就是说，底层图是未知的，需要从数据中推断出来。第二研究领域主要应用于空间流行病学。在这种情况下，ggm通常被称为高斯马尔可夫随机场(GMRFs)。下面的图被假定为已知的:顶点对应地理区域，而边与被认为是彼此相邻的区域相关联(例如，如果它们共享一个边界)。在这个演讲中，我们介绍了多路高斯图形模型，这些模型将时空流行病学推断的统计方法与一般GGMs的文献结合起来。提议的工作的新颖性包括在大量统计工具的收集中增加了G-Wishart分布，这些统计工具用于建模多变量区域数据。与描述地理的固定图形相反，在数据的其他维度上，与图形确定相关的固有不确定性。我们新的空间流行病学方法允许同时使用GGMs来表示已知的空间依赖关系，并确定数据其他维度中的未知依赖关系。与Alex Lenkoski和Abel Rodriguez合作。
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| 课程简介: |
The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying graph is unknown and needs to be inferred from the data. The second research domain dominates the applications in spatial epidemiology. In this context GGMs are typically referred to as Gaussian Markov random fields (GMRFs). Here the underlying graph is assumed to be known: the vertices correspond to geographical areas, while the edges are associated with areas that are considered to be neighbors of each other (e.g., if they share a border). In this talk we introduce multi-way Gaussian graphical models that unify the statistical approaches to inference for spatiotemporal epidemiology with the literature on general GGMs. The novelty of the proposed work consists of the addition of the G-Wishart distribution to the substantial collection of statistical tools used to model multivariate areal data. As opposed to fixed graphs that describe geography, there is an inherent uncertainty related to graph determination across the other dimensions of the data. Our new class of methods for spatial epidemiology allow the simultaneous use of GGMs to represent known spatial dependencies and to determine unknown dependencies in the other dimensions of the data. Joint work with Alex Lenkoski and Abel Rodriguez.
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| 关 键 词: |
多元高斯图模型; 多元格子数据
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| 课程来源: |
视频讲座网
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| 最后编审: |
2021-02-10：nkq
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| 阅读次数: |
61
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