An information-geometric framework for statistical inferences in the neural spike train space

Abstract

Statistical inferences are essentially important in analyzing neural spike trains in computational neuroscience. Current approaches have followed a general inference paradigm where a parametric probability model is often used to characterize the temporal evolution of the underlying stochastic processes. To directly capture the overall variability and distribution in the space of the spike trains, we focus on a data-driven approach where statistics are defined and computed in the function space in which spike trains are viewed as individual points. To this end, we at first develop a parametrized family of metrics that takes into account different warpings in the time domain and generalizes several currently used spike train distances. These new metrics are essentially penalized L ( p ) norms, involving appropriate functions of spike trains, with penalties associated with time-warping. The notions of means and variances of spike trains are then defined based on the new metrics when p = 2 (corresponding to the "Euclidean distance"). Using some restrictive conditions, we present an efficient recursive algorithm, termed Matching-Minimization algorithm, to compute the sample mean of a set of spike trains with arbitrary numbers of spikes. The proposed metrics as well as the mean spike trains are demonstrated using simulations as well as an experimental recording from the motor cortex. It is found that all these methods achieve desirable performance and the results support the success of this novel framework.

Statistical Analysis and Decoding of Neural Activity in the Rodent Geniculate Ganglion Using a Metric-Based Inference System

“…This metric, d 2 , taken from Wu and Srivastava [44] corresponds to the classical “Euclidean distance” between two spike trains. This metric is also closely related to the commonly used…”

“…We defined the sample mean of a set of spike trains using the Karcher mean with the d 2 metric [44]. Given a set of spike trains S 1 , S 2 , …, S N , their sample mean S * is defined as follows: …”

“…The framework becomes fully elastic in the time domain and this leads to a more intuitive distance. An efficient and convergent procedure, Matching-Minimization (MM) Algorithm, was constructed to compute the mean in this case [44]. For arbitrary value of λ (> 0), we need to update the number of spikes as well as their locations during the computation.…”

“…Wu and Srivastava [44] have proposed a novel metric to measure distance between spike trains. This metric corresponds to the conventional Euclidean distance in the function space.…”

Kernel Analysis for Estimating the Connectivity of a Network with Event Sequences

“…As an alternative, they introduced L p distances for spike trains [7]. Wu and Srivastava discussed spike train distances as metrics in a Riemannian space [47]. Chi et al modeled spiking activity as a sequence of commonly appearing templates and intervals between them, where spike patterns within each template are invariant, while the interval length between successive templates varies [4].…”