Department of Electrical Engineering, Indian Institute of Science, Bangalore, India.
Neural Comput. 2010 Apr;22(4):1025-59. doi: 10.1162/neco.2009.12-08-928.
We consider the problem of detecting statistically significant sequential patterns in multineuronal spike trains. These patterns are characterized by ordered sequences of spikes from different neurons with specific delays between spikes. We have previously proposed a data-mining scheme to efficiently discover such patterns, which occur often enough in the data. Here we propose a method to determine the statistical significance of such repeating patterns. The novelty of our approach is that we use a compound null hypothesis that not only includes models of independent neurons but also models where neurons have weak dependencies. The strength of interaction among the neurons is represented in terms of certain pair-wise conditional probabilities. We specify our null hypothesis by putting an upper bound on all such conditional probabilities. We construct a probabilistic model that captures the counting process and use this to derive a test of significance for rejecting such a compound null hypothesis. The structure of our null hypothesis also allows us to rank-order different significant patterns. We illustrate the effectiveness of our approach using spike trains generated with a simulator.
我们考虑在多神经元尖峰火车中检测统计学上显著的顺序模式的问题。这些模式的特征是来自不同神经元的尖峰以特定的延迟顺序排列，并且在尖峰之间具有特定的延迟。我们之前已经提出了一种数据挖掘方案，以有效地发现这些在数据中经常出现的模式。在这里，我们提出了一种确定这种重复模式的统计显著性的方法。我们方法的新颖之处在于，我们使用了一个复合的零假设，不仅包括独立神经元的模型，还包括神经元具有弱依赖性的模型。神经元之间相互作用的强度用某些成对条件概率来表示。我们通过对所有这些条件概率设置上限来指定我们的零假设。我们构建了一个捕获计数过程的概率模型，并使用该模型来推导出拒绝这种复合零假设的显着性检验。我们的零假设的结构还允许我们对不同的显著模式进行排序。我们使用带有模拟器生成的尖峰火车来说明我们方法的有效性。
