Oscillating neural circuits: Phase, amplitude, and the complex normal distribution

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Konrad N. Urban, Heejong Bong, Josue Orellana, Robert E. Kass
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引用次数: 2

Abstract

Multiple oscillating time series are typically analyzed in the frequency domain, where coherence is usually said to represent the magnitude of the correlation between two signals at a particular frequency. The correlation being referenced is complex-valued and is similar to the real-valued Pearson correlation in some ways but not others. We discuss the dependence among oscillating series in the context of the multivariate complex normal distribution, which plays a role for vectors of complex random variables analogous to the usual multivariate normal distribution for vectors of real-valued random variables. We emphasize special cases that are valuable for the neural data we are interested in and provide new variations on existing results. We then introduce a complex latent variable model for narrowly band-pass-filtered signals at some frequency, and show that the resulting maximum likelihood estimate produces a latent coherence that is equivalent to the magnitude of the complex canonical correlation at the given frequency. We also derive an equivalence between partial coherence and the magnitude of complex partial correlation, at a given frequency. Our theoretical framework leads to interpretable results for an interesting multivariate dataset from the Allen Institute for Brain Science.

Abstract Image

振荡神经回路:相位、振幅和复正态分布
通常在频域中分析多个振荡时间序列,其中相干性通常被认为表示特定频率下两个信号之间的相关性的大小。所引用的相关性是复值的,在某些方面与实值Pearson相关性相似,但在其他方面则不同。我们在多元复正态分布的背景下讨论了振荡序列之间的依赖关系,它对复随机变量的向量起着类似于实值随机变量向量的通常多元正态分布的作用。我们强调对我们感兴趣的神经数据有价值的特殊情况,并对现有结果提供新的变化。然后,我们为某些频率下的窄带通滤波信号引入了一个复杂的潜在变量模型,并表明所得到的最大似然估计产生的潜在相干性相当于给定频率下的复杂典型相关的幅度。在给定频率下,我们还推导出部分相干和复部分相关量级之间的等价关系。我们的理论框架为艾伦脑科学研究所的一个有趣的多元数据集带来了可解释的结果。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
62
审稿时长
>12 weeks
期刊介绍: The Canadian Journal of Statistics is the official journal of the Statistical Society of Canada. It has a reputation internationally as an excellent journal. The editorial board is comprised of statistical scientists with applied, computational, methodological, theoretical and probabilistic interests. Their role is to ensure that the journal continues to provide an international forum for the discipline of Statistics. The journal seeks papers making broad points of interest to many readers, whereas papers making important points of more specific interest are better placed in more specialized journals. The levels of innovation and impact are key in the evaluation of submitted manuscripts.
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