Discrimination with Spike Times and ISI Distributions

We study the discrimination capability of spike time sequences using the Chernoff distance as a metric. We assume that spike sequences are generated by renewal processes and study how the Chernoff distance depends on the shape of interspike interval (ISI) distribution. First, we consider a lower bound to the Chernoff distance because it has a simple closed form. Then we consider specific models of ISI distributions such as the gamma, inverse gaussian (IG), exponential with refractory period (ER), and that of the leaky integrate-and-fire (LIF) neuron. We found that the discrimination capability of spike times strongly depends on high-order moments of ISI and that it is higher when the spike time sequence has a larger skewness and a smaller kurtosis. High variability in terms of coefficient of variation (CV) does not necessarily mean that the spike times have less discrimination capability. Spike sequences generated by the gamma distribution have the minimum discrimination capability for a given mean and variance of ISI. We used series expansions to calculate the mean and variance of ISIs for LIF neurons as a function of the mean input level and the input noise variance. Spike sequences from an LIF neuron are more capable of discrimination than those of IG and gamma distributions when the stationary voltage level is close to the neuron's threshold value of the neuron.

[1]  Susanne Ditlevsen,et al.  Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  H. Hasegawa,et al.  Responses of a Hodgkin-Huxley neuron to various types of spike-train inputs. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  William Bialek,et al.  Entropy and Information in Neural Spike Trains , 1996, cond-mat/9603127.

[4]  Yutaka Sakai,et al.  The Ornstein-Uhlenbeck Process Does Not Reproduce Spiking Statistics of Neurons in Prefrontal Cortex , 1999, Neural Computation.

[5]  J. Victor.  Binless strategies for estimation of information from neural data. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Shun-ichi Amari,et al.  Methods of information geometry , 2000 .

[7]  Don H. Johnson,et al.  Information-Theoretic Analysis of Neural Coding , 2004, Journal of Computational Neuroscience.

[8]  Luigi M. Ricciardi,et al.  On the parameter estimation for diffusion models of single neuron's activities , 1995, Biological Cybernetics.

[9]  Christof Koch,et al.  The Impact of Spike Timing Variability on the Signal-Encoding Performance of Neural Spiking Models , 2002, Neural Computation.

[10]  H Sompolinsky,et al.  Simple models for reading neuronal population codes. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Peter F. Rowat,et al.  Interspike Interval Statistics in the Stochastic Hodgkin-Huxley Model: Coexistence of Gamma Frequency Bursts and Highly Irregular Firing , 2007, Neural Computation.

[12]  C. van Vreeswijk,et al.  Information transmission with renewal neurons , 2001, Neurocomputing.

[13]  R. Shapley,et al.  Information Tuning of Populations of Neurons in Primary Visual Cortex , 2004, The Journal of Neuroscience.

[14]  Benjamin Lindner,et al.  Interspike interval statistics of neurons driven by colored noise. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[16]  Kwee-Bo Sim,et al.  Brain-Computer Interface based on Changes of EEG on Broca's Area , 2009 .