线性-非线性模型估计目标函数的比较
Comparison of objective functions for estimating linear-nonlinear models
摘要：
本文比较了一个家庭的方法来表征神经功能的选择性与自然刺激的线性-非线性模型的框架。在该模型中，神经放电率是少量相关刺激成分的非线性函数。通过最大化目标函数族中的一个，不同阶数的Renyi分歧，可以找到相关的刺激维度。我们表明，最大限度地提高其中之一，Renyi散度的顺序为2，相当于最小二乘拟合的线性-非线性模型的神经数据。接下来，我们推导出重建误差在相关的尺寸发现最大化Renyi分歧的任意顺序的渐近极限的大尖峰数。我们发现，最小的误差得到的Renyi分歧的顺序1，也被称为Kullback-Leibler分歧。这对应于通过最大化互信息来找到相关维度。我们在数值上测试了这些优化方案在模型视觉神经元的低信噪比（少量尖峰和增加的神经噪声）下的表现。我们发现，优化方案的基础上，无论是最小二乘拟合或信息最大化表现良好，即使当尖峰的数量是小的。信息最大化提供了轻微的，但显着，更好的重建比最小二乘拟合。这使得寻找相关维度的问题，以及有损压缩的问题，其中一个例子，信息理论的措施是没有更多的数据限制比那些来自最小二乘法。
英文摘要：
This paper compares a family of methods for characterizing neural feature selectivity with natural stimuli in the framework of the linear-nonlinear model. In this model, the neural firing rate is a nonlinear function of a small number of relevant stimulus components. The relevant stimulus dimensions can be found by maximizing one of the family of objective functions, Renyi divergences of different orders. We show that maximizing one of them, Renyi divergence of order 2, is equivalent to least-square fitting of the linear-nonlinear model to neural data. Next, we derive reconstruction errors in relevant dimensions found by maximizing Renyi divergences of arbitrary order in the asymptotic limit of large spike numbers. We find that the smallest rrors are obtained with Renyi divergence of order 1, also known as Kullback-Leibler divergence. This corresponds to finding relevant dimensions by maximizing mutual information. We numerically test how these optimization schemes perform in the regime of low signal-to-noise ratio (small number of spikes and increasing neural noise) for model visual neurons. We find that optimization schemes based on either least square fitting or information maximization perform well even when number of spikes is small. Information maximization provides slightly, but significantly, better reconstructions than least square fitting. This makes the problem of finding relevant dimensions, together with the problem of lossy compression, one of examples where information-theoretic measures are no more data limited than those derived from least squares.
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