Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
Neural Comput. 2010 May;22(5):1231-44. doi: 10.1162/neco.2010.03-09-982.
Generalized linear models are an increasingly common approach for spike train data analysis. For the logistic and Poisson models, one possible difficulty is that iterative algorithms for computing parameter estimates may not converge because of certain data configurations. For the logistic model, these configurations are called complete and quasi-complete separation. We show that these features are likely to occur because of refractory periods of neurons. We use an example to study how standard software deals with this difficulty. For the Poisson model, we show that the same difficulties arise, this time possibly due to bursting or specifics of the binning. We characterize the nonconvergent configurations for both models, show that they can be detected by linear programming methods, and discuss possible remedies.
广义线性模型是一种越来越常见的尖峰时间序列数据分析方法。对于逻辑斯谛模型和泊松模型，一种可能的困难是，由于某些数据配置，用于计算参数估计的迭代算法可能无法收敛。对于逻辑斯谛模型，这些配置称为完全和准完全分离。我们表明，由于神经元的不应期，这些特征很可能出现。我们使用一个例子来研究标准软件如何处理这个困难。对于泊松模型，我们表明，同样的困难也会出现，这次可能是由于爆发或分箱的具体情况。我们对这两个模型的不可收敛配置进行了特征化，表明它们可以通过线性规划方法检测到，并讨论了可能的补救措施。
