Beyond GLMs: a generative mixture modeling approach to neural system identification.
Beyond GLMs: a generative mixture modeling approach to neural system identification.
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DOI：
10.1371/journal.pcbi.1003356
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发表时间：
2013
影响因子：
4.3
通讯作者：
Bethge M
中科院分区：
文献类型：
--
作者：
Theis L;Chagas AM;Arnstein D;Schwarz C;Bethge M
广义线性模型(GLMS)是一种常用的神经元放电反应的概率表征方法。虽然GLM因其计算处理能力而具有吸引力，但它们也强加了强有力的假设，因此只允许发现有限范围的刺激-反应关系。存在其他方法，这些方法只做出非常弱的假设，但不能很好地适应高维刺激空间。在这里，我们寻求一种能够在两个极端之间优雅地进行内插的方法。通过假设尖峰触发和非尖峰触发分布可以用高斯混合来充分表示，我们扩展了GLM的两个常用的特例--线性模型和二次模型。因为我们从生成性的角度得出该模型，所以它的组成部分很容易解释，因为它们对应于例如尖峰触发分布和尖峰间隔分布。该模型能够用比基于直方图的方法等其他方法少得多的参数来捕捉高维刺激的复杂依赖关系。增加的灵活性是以非凹对数可能性为代价的。我们表明，在实践中，这并不是一个问题，基于混合的模型能够比广义线性和二次模型表现得更好。感觉系统神经科学的一个基本目标是描述神经反应和外部刺激之间的功能关系。特别令人感兴趣的是单电池的非线性响应特性。然而，诸如广义线性建模之类的固有线性方法可用于通过为刺激选择适当的特征空间来拟合非线性行为。然而，这要求人们已经对细胞的非线性性质有了很好的了解，而更灵活的方法对于描述意外的非线性行为是必要的。在这项工作中，我们提出了一些常用的广义线性模型的推广，使我们能够从记录的数据中自动提取复杂的刺激-反应关系。我们表明，我们的模型可以在数量和质量上比广义线性和二次型模型有很大的改进，我们以大鼠胡须系统的初级传入为例进行了说明。
Generalized linear models (GLMs) represent a popular choice for the probabilistic characterization of neural spike responses. While GLMs are attractive for their computational tractability, they also impose strong assumptions and thus only allow for a limited range of stimulus-response relationships to be discovered. Alternative approaches exist that make only very weak assumptions but scale poorly to high-dimensional stimulus spaces. Here we seek an approach which can gracefully interpolate between the two extremes. We extend two frequently used special cases of the GLM—a linear and a quadratic model—by assuming that the spike-triggered and non-spike-triggered distributions can be adequately represented using Gaussian mixtures. Because we derive the model from a generative perspective, its components are easy to interpret as they correspond to, for example, the spike-triggered distribution and the interspike interval distribution. The model is able to capture complex dependencies on high-dimensional stimuli with far fewer parameters than other approaches such as histogram-based methods. The added flexibility comes at the cost of a non-concave log-likelihood. We show that in practice this does not have to be an issue and the mixture-based model is able to outperform generalized linear and quadratic models. An essential goal of sensory systems neuroscience is to characterize the functional relationship between neural responses and external stimuli. Of particular interest are the nonlinear response properties of single cells. Inherently linear approaches such as generalized linear modeling can nevertheless be used to fit nonlinear behavior by choosing an appropriate feature space for the stimulus. This requires, however, that one has already obtained a good understanding of a cells nonlinear properties, whereas more flexible approaches are necessary for the characterization of unexpected nonlinear behavior. In this work, we present a generalization of some frequently used generalized linear models which enables us to automatically extract complex stimulus-response relationships from recorded data. We show that our model can lead to substantial quantitative and qualitative improvements over generalized linear and quadratic models, which we illustrate on the example of primary afferents of the rat whisker system.
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影响因子：
3.2
作者：
Gerwinn S;Macke JH;Bethge M
通讯作者：
Bethge M
影响因子：
64.8
作者：
Pillow JW;Shlens J;Paninski L;Sher A;Litke AM;Chichilnisky EJ;Simoncelli EP
通讯作者：
Simoncelli EP
影响因子：
2.5
作者：
Fairhall, Adrienne L.;Burlingame, C. Andrew;Berry, Michael J., II
通讯作者：
Berry, Michael J., II
影响因子：
4.3
作者：
Fitzgerald JD;Rowekamp RJ;Sincich LC;Sharpee TO
通讯作者：
Sharpee TO
影响因子：
7.8
作者：
Paninski, L
通讯作者：
Paninski, L