Paper Info
Title
Spike train probability models for stimulus-driven leaky integrate-and-fire neurons.
Abstract
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.
Year
DOI
Venue
2008
10.1162/neco.2008.06-07-540
Neural Computation
Keywords
Field
DocType
TRRP model,spike train,spike train data,m-IMI model,better fit,time-varying stimulus,point process model,LIF spike train,LIF spike train variability,actual spike train data,spike train probability model,stimulus-driven leaky integrate-and-fire neuron
Renewal theory,Spike train,Biological system,Markov model,Point process,Markov chain,Models of neural computation,Probability distribution,Artificial intelligence,Mathematical model,Mathematics,Machine learning
Journal
Volume
Issue
ISSN
20
7
1530-888X
Citations 
PageRank 
References 
7
0.53
6
Authors
2
Name
Order
Citations
PageRank
Shinsuke Koyama1948.84
Robert E. Kass232843.43