Kernel bandwidth optimization in spike rate estimation.
Kernel bandwidth optimization in spike rate estimation.
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DOI：
10.1007/s10827-009-0180-4
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发表时间：
2010-08
影响因子：
1.2
通讯作者：
Shinomoto S
中科院分区：
文献类型：
--
作者：
Shimazaki H;Shinomoto S
核平滑器和时间直方图是用于估计尖峰发生的瞬时速率的经典工具。最近，我们建立了一种方法来选择的时间直方图的箱宽度，基于最小化的原则，估计率和未知的基础率之间的平均积分平方误差（MISE）。在这里，我们将相同的优化原理应用于核密度估计，以选择核的宽度或“带宽”，并进一步扩展算法以允许可变带宽，与数据一致。可变核有可能准确地把握非平稳现象，例如我们在神经科学中经常遇到的放电率的突然变化。为了避免由于过度自由而可能发生的过拟合，我们引入了带宽可变性的刚度常数。我们的方法自动调整刚度常数，从而适应整个尖峰数据集。据透露，经典的内核平滑器可能会表现出良好的拟合相媲美，甚至更好，现代先进的速率估计方法，只要适当地选择带宽为一组给定的尖峰数据，根据这里提出的优化方法。
Kernel smoother and a time-histogram are classical tools for estimating an instantaneous rate of spike occurrences. We recently established a method for selecting the bin width of the time-histogram, based on the principle of minimizing the mean integrated square error (MISE) between the estimated rate and unknown underlying rate. Here we apply the same optimization principle to the kernel density estimation in selecting the width or “bandwidth” of the kernel, and further extend the algorithm to allow a variable bandwidth, in conformity with data. The variable kernel has the potential to accurately grasp non-stationary phenomena, such as abrupt changes in the firing rate, which we often encounter in neuroscience. In order to avoid possible overfitting that may take place due to excessive freedom, we introduced a stiffness constant for bandwidth variability. Our method automatically adjusts the stiffness constant, thereby adapting to the entire set of spike data. It is revealed that the classical kernel smoother may exhibit goodness-of-fit comparable to, or even better than, that of modern sophisticated rate estimation methods, provided that the bandwidth is selected properly for a given set of spike data, according to the optimization methods presented here.
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