多变量尖峰观测演化谱的多锥分析
Multitaper Analysis of Evolutionary Spectra from Multivariate Spiking Observations
摘要：
提取尖峰活动背后的神经过程的频谱表示是理解大脑节律如何介导认知功能的关键。虽然连续时间序列的谱估计已经得到了很好的研究，但基于尖峰观测值推断潜在非平稳过程的谱表示是一个具有挑战性的问题。在本文中，我们解决这个问题，通过开发一个多锥度谱估计方法，可以直接应用于多变量尖峰观测，以提取潜在的非平稳过程，驱动尖峰活动的进化谱密度，基于点过程理论。我们建立了理论界的偏差方差权衡建议的估计。最后，我们比较了我们提出的技术与现有的方法，使用模拟研究和应用程序的实际数据，这揭示了显着的收益的偏差方差权衡的性能。
英文摘要：
Extracting the spectral representations of the neural processes that underlie spiking activity is key to understanding how the brain rhythms mediate cognitive functions. While spectral estimation of continuous time-series is well studied, inferring the spectral representation of latent non-stationary processes based on spiking observations is a challenging problem. In this paper, we address this issue by developing a multitaper spectral estimation methodology that can be directly applied to multivariate spiking observations in order to extract the evolutionary spectral density of the latent non-stationary processes that drive spiking activity, based on point process theory. We establish theoretical bounds on the bias-variance trade-off of the proposed estimator. Finally, we compare the performance of our proposed technique with existing methods using simulation studies and application to real data, which reveal significant gains in terms of the bias-variance trade-off.
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