Assessing Goodness-of-Fit in Marked Point Process Models of Neural Population Coding via Time and Rate Rescaling

Abstract

Marked point process models have recently been used to capture the coding properties of neural populations from multiunit electrophysiological recordings without spike sorting. These clusterless models have been shown in some instances to better describe the firing properties of neural populations than collections of receptive field models for sorted neurons and to lead to better decoding results. To assess their quality, we previously proposed a goodness-of-fit technique for marked point process models based on time rescaling, which for a correct model produces a set of uniform samples over a random region of space. However, assessing uniformity over such a region can be challenging, especially in high dimensions. Here, we propose a set of new transformations in both time and the space of spike waveform features, which generate events that are uniformly distributed in the new mark and time spaces. These transformations are scalable to multidimensional mark spaces and provide uniformly distributed samples in hypercubes, which are well suited for uniformity tests. We discuss the properties of these transformations and demonstrate aspects of model fit captured by each transformation. We also compare multiple uniformity tests to determine their power to identify lack-of-fit in the rescaled data. We demonstrate an application of these transformations and uniformity tests in a simulation study. Proofs for each transformation are provided in the appendix.

An Investigation on Spiking Neural Networks Based on the Izhikevich Neuronal Model: Spiking Processing and Hardware Approach

“…The neuron is the basic part of this system that can connect to other neurons by a connection called a synapse. Indeed, neurons are responsible for receiving, processing, and sending information [129][130][131][132][133][134][135][136][137].…”

Bayesian nonparametric (non-)renewal processes for analyzing neural spike train variability

“…Combining the latter alongside observed covariates [48] with our point process provides a powerful framework for capturing correlations [81], which can have significant impact on neural coding [56]. To perform goodness-of-fit tests, the Kolmogorov-Smirnov test with time-rescaling can be extended to the multivariate case [30, 92].…”

From End to End: Gaining, Sorting, and Employing High-Density Neural Single Unit Recordings

“…Spike sorting indeed does not have to be compulsory when population activity is targeted (Trautmann et al, 2019 ); therefore brain-computer interface systems that engage in multi-unit activity may settle for less complex preprocessing techniques. Such a method is “binning,” by which firing rates are estimated in a fixed time window (Ahmadi et al, 2020 ), and with marked point models (Yousefi et al, 2020 ) or interspike interval histograms combined with power spectrum density estimation, complete firing patterns can be investigated (Guo et al, 2020 ): these methods are advantageous when tuning curves of single neurons may be distributed bimodally, such as in the case of murine head direction cells (Liu and Lengyel, 2021 ). Whenever applying a clustering-free method, one should keep in mind that its goodness-of-fit evaluation may differ from mainstream clustering algorithms (Tao et al, 2018 ).…”