A point-process matched filter for event detection and decoding from population spike trains

Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistical methods based on point process models of spike trains provide a wide range of data-analytical techniques. Two simplified point process models have been introduced in the literature: the time-rescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (m-IMI) model. In this letter we investigate the extent to which the TRRP and m-IMI models are able to fit spike trains produced by stimulus-driven leaky integrate-and-fire (LIF) neurons. With a constant stimulus, the LIF spike train is a renewal process, and the m-IMI and TRRP models will describe accurately the LIF spike train variability. With a time-varying stimulus, the probability of spiking under all three of these models depends on both the experimental clock time relative to the stimulus and the time since the previous spike, but it does so differently for the LIF, m-IMI, and TRRP models. We assessed the distance between the LIF model and each of the two empirical models in the presence of a time-varying stimulus. We found that while lack of fit of a Poisson model to LIF spike train data can be evident even in small samples, the m-IMI and TRRP models tend to fit well, and much larger samples are required before there is statistical evidence of lack of fit of the m-IMI or TRRP models. We also found that when the mean of the stimulus varies across time, the m-IMI model provides a better fit to the LIF data than the TRRP, and when the variance of the stimulus varies across time, the TRRP provides the better fit.

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A Bayesian Generative Model of Vestibular Afferent Neuron Spiking

10.1101/2020.02.03.933150 ◽

2020 ◽

Author(s):

Michael Paulin ◽

Kiri Pullar ◽

Larry Hoffman

Keyword(s):

Bayesian Inference ◽

State Estimation ◽

Point Process ◽

Semicircular Canal ◽

Spike Trains ◽

Generative Model ◽

Neural Computation ◽

Neuronal Membrane ◽

Afferent Neuron ◽

Nervous Systems

AbstractUsing an information criterion to evaluate models fitted to spike train data from chinchilla semicircular canal afferent neurons, we found that the superficially complex functional organization of the canal nerve branch can be accurately quantified in an elegant mathematical model with only three free parameters. Spontaneous spike trains are samples from stationary renewal processes whose interval distributions are Exwald distributions, convolutions of Inverse Gaussian and Exponential distributions. We show that a neuronal membrane compartment is a natural computer for calculating parameter likelihoods given samples from a point process with such a distribution, which may facilitate fast, accurate, efficient Bayesian neural computation for estimating the kinematic state of the head. The model suggests that Bayesian neural computation is an aspect of a more general principle that has driven the evolution of nervous system design, the energy efficiency of biological information processing.Significance StatementNervous systems ought to have evolved to be Bayesian, because Bayesian inference allows statistically optimal evidence-based decisions and actions. A variety of circumstantial evidence suggests that animal nervous systems are indeed capable of Bayesian inference, but it is unclear how they could do this. We have identified a simple, accurate generative model of vestibular semicircular canal afferent neuron spike trains. If the brain is a Bayesian observer and a Bayes-optimal decision maker, then the initial stage of processing vestibular information must be to compute the posterior density of head kinematic state given sense data of this form. The model suggests how neurons could do this. Head kinematic state estimation given point-process inertial data is a well-defined dynamical inference problem whose solution formed a foundation for vertebrate brain evolution. The new model provides a foundation for developing realistic, testable spiking neuron models of dynamical state estimation in the vestibulo-cerebellum, and other parts of the Bayesian brain.

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Robust point-process Granger causality analysis in presence of exogenous temporal modulations and trial-by-trial variability in spike trains

PLoS Computational Biology ◽

10.1371/journal.pcbi.1007675 ◽

2021 ◽

Vol 17 (1) ◽

pp. e1007675

Author(s):

Antonino Casile ◽

Rose T. Faghih ◽

Emery N. Brown

Keyword(s):

Granger Causality ◽

Point Process ◽

Temporal Structure ◽

Temporal Variations ◽

Spike Trains ◽

Neuronal Firing ◽

Connectivity Pattern ◽

Relative Reduction ◽

Neuronal Responses ◽

Neurophysiological Studies

Assessing directional influences between neurons is instrumental to understand how brain circuits process information. To this end, Granger causality, a technique originally developed for time-continuous signals, has been extended to discrete spike trains. A fundamental assumption of this technique is that the temporal evolution of neuronal responses must be due only to endogenous interactions between recorded units, including self-interactions. This assumption is however rarely met in neurophysiological studies, where the response of each neuron is modulated by other exogenous causes such as, for example, other unobserved units or slow adaptation processes. Here, we propose a novel point-process Granger causality technique that is robust with respect to the two most common exogenous modulations observed in real neuronal responses: within-trial temporal variations in spiking rate and between-trial variability in their magnitudes. This novel method works by explicitly including both types of modulations into the generalized linear model of the neuronal conditional intensity function (CIF). We then assess the causal influence of neuron i onto neuron j by measuring the relative reduction of neuron j’s point process likelihood obtained considering or removing neuron i. CIF’s hyper-parameters are set on a per-neuron basis by minimizing Akaike’s information criterion. In synthetic data sets, generated by means of random processes or networks of integrate-and-fire units, the proposed method recovered with high accuracy, sensitivity and robustness the underlying ground-truth connectivity pattern. Application of presently available point-process Granger causality techniques produced instead a significant number of false positive connections. In real spiking responses recorded from neurons in the monkey pre-motor cortex (area F5), our method revealed many causal relationships between neurons as well as the temporal structure of their interactions. Given its robustness our method can be effectively applied to real neuronal data. Furthermore, its explicit estimate of the effects of unobserved causes on the recorded neuronal firing patterns can help decomposing their temporal variations into endogenous and exogenous components.

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