Extracting the spectral representations of neural processes that underlie spiking activity is key to understanding how 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 challenging due to the underlying nonlinearities that limit the spectrotemporal resolution of existing methods. 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 semi-stationary spectral density of the latent non-stationary processes that govern spiking activity. We establish theoretical bounds on the bias-variance trade-off of our proposed estimator. Finally, application of our proposed technique to simulated and real data reveals significant performance gains over existing methods.

中文翻译：

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多变量神经元尖峰观察的半稳态光谱的多锥度分析


提取尖峰活动背后的神经过程的光谱表示是理解大脑节律如何调节认知功能的关键。虽然连续时间序列的谱估计得到了很好的研究，但由于潜在的非线性限制了现有方法的谱时间分辨率，因此基于尖峰观测推断潜在非平稳过程的谱表示具有挑战性。在本文中，我们通过开发一种多锥谱估计方法来解决这个问题，该方法可以直接应用于多元尖峰观测，以提取控制尖峰活动的潜在非平稳过程的半平稳谱密度。我们为我们提出的估计量的偏差-方差权衡建立了理论界限。最后，将我们提出的技术应用于模拟和真实数据表明比现有方法有显着的性能提升。