Technische Universität Berlin, Berlin, Germany.
PLoS Comput Biol. 2012;8(6):e1002539. doi: 10.1371/journal.pcbi.1002539. Epub 2012 Jun 7.
Evaluating the importance of higher-order correlations of neural spike counts has been notoriously hard. A large number of samples are typically required in order to estimate higher-order correlations and resulting information theoretic quantities. In typical electrophysiology data sets with many experimental conditions, however, the number of samples in each condition is rather small. Here we describe a method that allows to quantify evidence for higher-order correlations in exactly these cases. We construct a family of reference distributions: maximum entropy distributions, which are constrained only by marginals and by linear correlations as quantified by the Pearson correlation coefficient. We devise a Monte Carlo goodness-of-fit test, which tests--for a given divergence measure of interest--whether the experimental data lead to the rejection of the null hypothesis that it was generated by one of the reference distributions. Applying our test to artificial data shows that the effects of higher-order correlations on these divergence measures can be detected even when the number of samples is small. Subsequently, we apply our method to spike count data which were recorded with multielectrode arrays from the primary visual cortex of anesthetized cat during an adaptation experiment. Using mutual information as a divergence measure we find that there are spike count bin sizes at which the maximum entropy hypothesis can be rejected for a substantial number of neuronal pairs. These results demonstrate that higher-order correlations can matter when estimating information theoretic quantities in V1. They also show that our test is able to detect their presence in typical in-vivo data sets, where the number of samples is too small to estimate higher-order correlations directly.
评估神经尖峰计数的高阶相关性一直是一项艰巨的任务。为了估计高阶相关性和由此产生的信息论量，通常需要大量的样本。然而，在具有许多实验条件的典型电生理数据集，每个条件下的样本数量通常很小。在这里，我们描述了一种方法，可以在这些情况下定量地证明高阶相关性的证据。我们构建了一组参考分布：最大熵分布，这些分布仅受边缘分布和线性相关性的限制，线性相关性由皮尔逊相关系数来量化。我们设计了一个蒙特卡罗拟合优度检验，用于检验对于给定的感兴趣的散度度量，实验数据是否导致拒绝零假设，即数据是由参考分布之一生成的。将我们的测试应用于人工数据表明，即使样本数量较少，高阶相关性对这些散度度量的影响也可以被检测到。随后，我们将我们的方法应用于在麻醉猫的初级视觉皮层上使用多电极阵列记录的尖峰计数数据，在适应实验中。使用互信息作为散度度量，我们发现对于大量神经元对，在某些尖峰计数 bin 大小下，可以拒绝最大熵假设。这些结果表明，高阶相关性在估计 V1 中的信息论量时可能很重要。它们还表明，我们的测试能够在典型的体内数据集，即样本数量太小而无法直接估计高阶相关性的情况下，检测到它们的存在。
