Samonds Jason M, Potetz Brian R, Lee Tai Sing
Center for the Neural Basis of Cognition and Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
Neural Comput. 2014 May;26(5):860-906. doi: 10.1162/NECO_a_00582. Epub 2014 Feb 20.
We propose using the statistical measurement of the sample skewness of the distribution of mean firing rates of a tuning curve to quantify sharpness of tuning. For some features, like binocular disparity, tuning curves are best described by relatively complex and sometimes diverse functions, making it difficult to quantify sharpness with a single function and parameter. Skewness provides a robust nonparametric measure of tuning curve sharpness that is invariant with respect to the mean and variance of the tuning curve and is straightforward to apply to a wide range of tuning, including simple orientation tuning curves and complex object tuning curves that often cannot even be described parametrically. Because skewness does not depend on a specific model or function of tuning, it is especially appealing to cases of sharpening where recurrent interactions among neurons produce sharper tuning curves that deviate in a complex manner from the feedforward function of tuning. Since tuning curves for all neurons are not typically well described by a single parametric function, this model independence additionally allows skewness to be applied to all recorded neurons, maximizing the statistical power of a set of data. We also compare skewness with other nonparametric measures of tuning curve sharpness and selectivity. Compared to these other nonparametric measures tested, skewness is best used for capturing the sharpness of multimodal tuning curves defined by narrow peaks (maximum) and broad valleys (minima). Finally, we provide a more formal definition of sharpness using a shape-based information gain measure and derive and show that skewness is correlated with this definition.
我们建议使用调谐曲线平均发放率分布的样本偏度的统计测量来量化调谐的锐度。对于某些特征，如双眼视差，调谐曲线最好用相对复杂且有时多样的函数来描述，这使得用单一函数和参数来量化锐度变得困难。偏度提供了一种稳健的非参数调谐曲线锐度测量方法，它对于调谐曲线的均值和方差是不变的，并且可以直接应用于广泛的调谐类型，包括简单的方向调谐曲线和复杂的物体调谐曲线，后者甚至常常无法用参数形式描述。由于偏度不依赖于特定的调谐模型或函数，对于神经元之间的递归相互作用产生比前馈调谐函数更尖锐且以复杂方式偏离的调谐曲线的锐化情况，它特别有吸引力。由于并非所有神经元的调谐曲线通常都能用单一参数函数很好地描述，这种模型独立性还允许将偏度应用于所有记录的神经元，从而最大化一组数据的统计功效。我们还将偏度与调谐曲线锐度和选择性的其他非参数测量方法进行了比较。与测试的这些其他非参数测量方法相比，偏度最适合用于捕捉由窄峰（最大值）和宽谷（最小值）定义的多峰调谐曲线的锐度。最后，我们使用基于形状的信息增益测量方法给出了锐度的更正式定义，并推导并表明偏度与该定义相关。
