Spectral methods for neural characterization using generalized quadratic models
Spectral methods for neural characterization using generalized quadratic models
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发表时间：
2013-12
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通讯作者：
Il-Su Park;Evan Archer;Nicholas J. Priebe;Jonathan W. Pillow
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作者：
Il-Su Park;Evan Archer;Nicholas J. Priebe;Jonathan W. Pillow
我们描述了一组快速，易于处理的方法，用于表征神经反应高维感官刺激使用的模型，我们称为广义二次模型（GQM）。GQM由一个低秩二次函数，其次是点非线性和指数族噪声。二次函数表征神经元的刺激选择性的一组线性感受野其次是二次组合规则，和可逆的非线性映射这个输出到所需的响应范围。GQM的特殊情况包括二阶沃尔泰拉模型[1，2]和椭圆线性-非线性-泊松模型[3]。在这里，我们表明，对于“规范形式”的GQM，谱分解的前两个响应加权矩产生近似的最大似然估计通过一个数量称为预期的对数似然。由此产生的理论概括了基于矩的估计量，例如尖峰触发的协方差，并且在高斯噪声的情况下，在一大类非高斯刺激分布下提供了封闭形式的估计量。我们表明，这些估计是快速的，并提供高精度的估计，远低于完全最大似然的计算成本。此外，GQM提供了一个自然的框架，在一个单一的模型内结合多维刺激敏感性和尖峰历史的依赖性。我们显示应用程序的模拟和尖峰数据使用细胞内记录的V1膜电位和细胞外记录的视网膜尖峰列车。
We describe a set of fast, tractable methods for characterizing neural responses to high-dimensional sensory stimuli using a model we refer to as the generalized quadratic model (GQM). The GQM consists of a low-rank quadratic function followed by a point nonlinearity and exponential-family noise. The quadratic function characterizes the neuron's stimulus selectivity in terms of a set linear receptive fields followed by a quadratic combination rule, and the invertible nonlinearity maps this output to the desired response range. Special cases of the GQM include the 2nd-order Volterra model [1, 2] and the elliptical Linear-Nonlinear-Poisson model [3]. Here we show that for "canonical form" GQMs, spectral decomposition of the first two response-weighted moments yields approximate maximum-likelihood estimators via a quantity called the expected log-likelihood. The resulting theory generalizes moment-based estimators such as the spike-triggered co-variance, and, in the Gaussian noise case, provides closed-form estimators under a large class of non-Gaussian stimulus distributions. We show that these estimators are fast and provide highly accurate estimates with far lower computational cost than full maximum likelihood. Moreover, the GQM provides a natural framework for combining multi-dimensional stimulus sensitivity and spike-history dependencies within a single model. We show applications to both analog and spiking data using intracellular recordings of V1 membrane potential and extracellular recordings of retinal spike trains.