A Computationally Efficient Method for Nonparametric Modeling of Neural Spiking Activity with Point Processes
A Computationally Efficient Method for Nonparametric Modeling of Neural Spiking Activity with Point Processes
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DOI：
10.1162/neco_a_00001-coleman
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发表时间：
2010-08-01
影响因子：
2.9
通讯作者：
Sarma, Sridevi S.
中科院分区：
文献类型：
--
作者：
Coleman, Todd P.;Sarma, Sridevi S.
点过程模型已被证明是有用的表征神经尖峰活动作为外在和内在因素的函数。大多数神经活动的点过程模型是参数化的，因为它们通常是可有效计算的。然而，如果实际的点过程并不在于假设的参数类的功能，误导性的推论可能会出现。非参数方法由于较少的假设而具有吸引力，但计算通常随着数据的大小而增长。我们提出了一种计算效率高的方法，非参数极大似然估计时的条件强度函数，它的特点是在其整体上的点过程，被假定为Lipschitz连续函数，但在其他任意。我们表明，通过利用多结构，问题变得有效地解决。接下来，我们演示了一个模型选择过程，以估计Lipshitz参数的数据，类似于最小描述长度原则，并证明我们的估计在适当的假设下的一致性。最后，我们说明了我们的方法的有效性与模拟神经尖峰数据，金鱼视网膜神经节神经数据，并记录在CA1海马神经元从清醒的行为大鼠的活动。对于模拟数据集，我们的方法揭示了一个更紧凑的表示条件强度函数时，它存在。对于金鱼和大鼠的神经数据集，我们表明，我们的非参数方法提供了一个上级的绝对拟合优度的措施，用于点过程比最常见的参数和样条为基础的方法。
Point-process models have been shown to be useful in characterizing neural spiking activity as a function of extrinsic and intrinsic factors. Most point-process models of neural activity are parametric, as they are often efficiently computable. However, if the actual point process does not lie in the assumed parametric class of functions, misleading inferences can arise. Nonparametric methods are attractive due to fewer assumptions, but computation in general grows with the size of the data. We propose a computationally efficient method for nonparametric maximum likelihood estimation when the conditional intensity function, which characterizes the point process in its entirety, is assumed to be a Lipschitz continuous function but otherwise arbitrary. We show that by exploiting much structure, the problem becomes efficiently solvable. We next demonstrate a model selection procedure to estimate the Lipshitz parameter from data, akin to the minimum description length principle and demonstrate consistency of our estimator under appropriate assumptions. Finally, we illustrate the effectiveness of our method with simulated neural spiking data, goldfish retinal ganglion neural data, and activity recorded in CA1 hippocampal neurons from an awake behaving rat. For the simulated data set, our method uncovers a more compact representation of the conditional intensity function when it exists. For the goldfish and rat neural data sets, we show that our nonparametric method gives a superior absolute goodness-of-fit measure used for point processes than the most common parametric and splines-based approaches.