Sparse Functional Dynamical Models—A Big Data Approach
针对神经集群的尖峰活动，提出一种稀疏函数动态模型，用Volterra级数展开描述多输入单输出的点过程，通过B样条和惩罚似然估计核函数，并利用大数据技术解决计算挑战，在大鼠海马数据上验证了性能。
Nonlinear dynamical systems are encountered in many areas of social science, natural science, and engineering, and are of particular interest for complex biological processes like the spiking activity of neural ensembles in the brain. To describe such spiking activity, we adapt the Volterra series expansion of an analytic function to account for the point-process nature of multiple inputs and a single output (MISO) in a neural ensemble. Our model describes the transformed spiking probability for the output as the sum of kernel-weighted integrals of the inputs. The kernel functions need to be identified and estimated, and both local sparsity (kernel functions may be zero on part of their support) and global sparsity (some kernel functions may be identically zero) are of interest. The kernel functions are approximated by B-splines and a penalized likelihood-based approach is proposed for estimation. Even for moderately complex brain functionality, the identification and estimation of this sparse functional dynamical model poses major computational challenges, which we address with big data techniques that can be implemented on a single, multi-core server. The performance of the proposed method is demonstrated using neural recordings from the hippocampus of a rat during open field tasks. Supplementary materials for this article are available online.