神经元尖峰序列非线性贝叶斯解码的粒子滤波方法

A. Kutschireiter, J. Pfister
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引用次数: 1

摘要

可以同时记录的神经元数量每七年翻一番。记录的神经元数量不断增加,为解决新问题和从记录中提取更高维度的刺激提供了可能性。将神经脉冲序列建模为点过程,从脉冲序列中提取动态信号的任务通常设置在非线性滤波理论的背景下。依赖于重要权值的粒子滤波方法是一种用数值方法解决滤波任务的通用算法,但是当问题的维数很高时,它们表现出一个严重的缺点:它们受到“维数诅咒”(COD)的影响,即特定性能所需的粒子数量随着可观察维数呈指数级增长。本文首先简要介绍了连续时间点过程观测滤波的理论。基于这一理论,我们从解析和数值两个方面研究了加权粒子滤波方法COD的原因:与连续时间观测的粒子滤波相似,点过程观测的COD是由于有效粒子数的衰减,当可观测维数增加时,这种效应更强。鉴于非加权粒子滤波方法在克服连续时间观测的COD方面的成功,我们引入了一种用于点过程观测的非加权粒子滤波器,即基于峰值的神经粒子滤波器(sNPF),并表明它随着维数的增加而表现出类似的有利尺度。进一步,我们从极大似然方法学习中推导出sNPF参数的规则。最后,我们使用一个简单的解码任务来说明sNPF的功能,并强调我们的推理和学习算法的一个可能的未来应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Particle-filtering approaches for nonlinear Bayesian decoding of neuronal spike trains
The number of neurons that can be simultaneously recorded doubles every seven years. This ever increasing number of recorded neurons opens up the possibility to address new questions and extract higher dimensional stimuli from the recordings. Modeling neural spike trains as point processes, this task of extracting dynamical signals from spike trains is commonly set in the context of nonlinear filtering theory. Particle filter methods relying on importance weights are generic algorithms that solve the filtering task numerically, but exhibit a serious drawback when the problem dimensionality is high: they are known to suffer from the 'curse of dimensionality' (COD), i.e. the number of particles required for a certain performance scales exponentially with the observable dimensions. Here, we first briefly review the theory on filtering with point process observations in continuous time. Based on this theory, we investigate both analytically and numerically the reason for the COD of weighted particle filtering approaches: Similarly to particle filtering with continuous-time observations, the COD with point-process observations is due to the decay of effective number of particles, an effect that is stronger when the number of observable dimensions increases. Given the success of unweighted particle filtering approaches in overcoming the COD for continuous- time observations, we introduce an unweighted particle filter for point-process observations, the spike-based Neural Particle Filter (sNPF), and show that it exhibits a similar favorable scaling as the number of dimensions grows. Further, we derive rules for the parameters of the sNPF from a maximum likelihood approach learning. We finally employ a simple decoding task to illustrate the capabilities of the sNPF and to highlight one possible future application of our inference and learning algorithm.
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