Roudi Yasser, Aurell Erik, Hertz John A
NORDITA Stockholm, Sweden.
Front Comput Neurosci. 2009 Nov 17;3:22. doi: 10.3389/neuro.10.022.2009. eCollection 2009.
Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data: knowledge of the mean values and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying and using pairwise models. We build on our previous work on the subject and study the relation between different methods for fitting these models and evaluating their quality. In particular, using data from simulated cortical networks we study how the quality of various approximate methods for inferring the parameters in a pairwise model depends on the time bin chosen for binning the data. We also study the effect of the size of the time bin on the model quality itself, again using simulated data. We show that using finer time bins increases the quality of the pairwise model. We offer new ways of deriving the expressions reported in our previous work for assessing the quality of pairwise models.
用于描述生物系统状态概率分布的统计模型通常用于降维。在这些模型中，成对模型非常有吸引力，部分原因是它们可以使用合理数量的数据进行拟合：了解系统中元素对之间的平均值和相关性就足够了。因此，毫不奇怪，近年来使用成对模型研究神经数据一直是许多研究的重点。在本文中，我们描述了如何运用统计物理学工具来研究和使用成对模型。我们基于之前在该主题上的工作，研究了拟合这些模型的不同方法与评估其质量之间的关系。特别是，我们使用来自模拟皮层网络的数据，研究了成对模型中各种近似推断参数方法的质量如何取决于为数据分箱选择的时间间隔。我们还使用模拟数据研究了时间间隔大小对模型质量本身的影响。我们表明，使用更精细的时间间隔可以提高成对模型的质量。我们提供了新的方法来推导我们之前工作中报告的用于评估成对模型质量的表达式。
