Efficient Optimization of Partition Scan Statistics via the Consecutive Partitions Property
Efficient Optimization of Partition Scan Statistics via the Consecutive Partitions Property
复制标题
通过连续分区属性有效优化分区扫描统计
DOI：
10.1080/10618600.2022.2077351
复制
发表时间：
2022
影响因子：
2.4
通讯作者：
Neill, Daniel B.
中科院分区：
文献类型：
--
作者：
Pehlivanian, Charles A.;Neill, Daniel B.
我们概括的空间和子集扫描统计从单一到多个子集的情况下。两个主要的方法来定义的对数似然比统计在单个子集的情况下，人口为基础的和期望为基础的扫描策略，被认为是导致风险分区和多个集群检测扫描统计，分别。我们表明，对于可分离指数族中的分布，风险划分扫描统计量可以表示为标准化计数和基线向量的缩放f偏差，而多集群检测扫描统计量可以表示为缩放Bregman偏差之和。然而，在任何一种情况下，通过对数据的所有分区进行穷举搜索来最大化扫描统计量需要指数时间。为了使这种优化计算上可行，我们证明了充分条件下，保证最佳分割是连续的。此连续分区属性将线性时间子集扫描属性从两个分区（检测到的子集和剩余数据元素）推广到多个分区的情况。虽然连续partitionings ofnelements到tpartitions规模，使其计算昂贵的larget，我们提出了一种动态规划方法，确定最佳的连续分区的时间，从而允许大规模的风险分区和多个集群检测问题的准确和有效的解决方案。最后，我们展示了检测性能和实际效用的分区扫描统计使用模拟和真实世界的数据。本文的补充材料可在网上查阅。
We generalize the spatial and subset scan statistics from the single to the multiple subset case. The two main approaches to defining the log-likelihood ratio statistic in the single subset case—the population-based and expectation-based scan statistics—are considered, leading to risk partitioning and multiple cluster detection scan statistics, respectively. We show that, for distributions in a separable exponential family, the risk partitioning scan statistic can be expressed as a scaledf-divergence of the normalized count and baseline vectors, and the multiple cluster detection scan statistic as a sum of scaled Bregman divergences. In either case, however, maximization of the scan statistic by exhaustive search over all partitionings of the data requires exponential time. To make this optimization computationally feasible, we prove sufficient conditions under which the optimal partitioning is guaranteed to be consecutive. This Consecutive Partitions Property generalizes the linear-time subset scanning property from two partitions (the detected subset and the remaining data elements) to the multiple partition case. While the number of consecutive partitionings ofnelements intotpartitions scales as, making it computationally expensive for larget, we present a dynamic programming approach which identifies the optimal consecutive partitioning intime, thus allowing for the exact and efficient solution of large-scale risk partitioning and multiple cluster detection problems. Finally, we demonstrate the detection performance and practical utility of partition scan statistics using simulated and real-world data. Supplementary materials for this article are available online.
DOI：
--
发表时间：
1965
期刊：
影响因子：
--
作者：
J. Naus
通讯作者：
J. Naus
影响因子：
1.1
作者：
Zhang, Zhenkui;Assuncao, Renato;Kulldorff, Martin
通讯作者：
Kulldorff, Martin