Nonparametric Modeling of Neural Point Processes via Stochastic Gradient Boosting Regression

Statistical nonparametric modeling tools that enable the discovery and approximation of functional forms (e.g., tuning functions) relating neural spiking activity to relevant covariates are desirable tools in neuroscience. In this article, we show how stochastic gradient boosting regression can be successfully extended to the modeling of spiking activity data while preserving their point process nature, thus providing a robust nonparametric modeling tool. We formulate stochastic gradient boosting in terms of approximating the conditional intensity function of a point process in discrete time and use the standard likelihood of the process to derive the loss function for the approximation problem. To illustrate the approach, we apply the algorithm to the modeling of primary motor and parietal spiking activity as a function of spiking history and kinematics during a two-dimensional reaching task. Model selection, goodness of fit via the time rescaling theorem, model interpretation via partial dependence plots, ranking of covariates according to their relative importance, and prediction of peri-event time histograms are illustrated and discussed. Additionally, we use the tenfold cross-validated log likelihood of the modeled neural processes (67 cells) to compare the performance of gradient boosting regression to two alternative approaches: standard generalized linear models (GLMs) and Bayesian P-splines with Markov chain Monte Carlo (MCMC) sampling. In our data set, gradient boosting outperformed both Bayesian P-splines (in approximately 90 of the cells) and GLMs (100). Because of its good performance and computational efficiency, we propose stochastic gradient boosting regression as an off-the-shelf nonparametric tool for initial analyses of large neural data sets (e.g., more than 50 cells; more than 105 samples per cell) with corresponding multidimensional covariate spaces (e.g., more than four covariates). In the cases where a functional form might be amenable to a more compact representation, gradient boosting might also lead to the discovery of simpler, parametric models.