A Comparison of Descriptive Models of a Single Spike Train by Information-Geometric Measure

In examining spike trains, different models are used to describe their structure. The different models often seem quite similar, but because they are cast in different formalisms, it is often difficult to compare their predictions. Here we use the information-geometric measure, an orthogonal coordinate representation of point processes, to express different models of stochastic point processes in a common coordinate system. Within such a framework, it becomes straightforward to visualize higher-order correlations of different models and thereby assess the differences between models. We apply the information-geometric measure to compare two similar but not identical models of neuronal spike trains: the inhomogeneous Markov and the mixture of Poisson models. It is shown that they differ in the second- and higher-order interaction terms. In the mixture of Poisson model, the second- and higher-order interactions are of comparable magnitude within each order, whereas in the inhomogeneous Markov model, they have alternating signs over different orders. This provides guidance about what measurements would effectively separate the two models. As newer models are proposed, they also can be compared to these models using information geometry.

[1]  Masato Inoue,et al.  Gene Interaction in DNA Microarray Data Is Decomposed by Information Geometric Measure , 2003, Bioinform..

[2]  H. C. Tuckwell,et al.  The significance of precisely replicating patterns in mammalian CNS spike trains , 1997, Neuroscience.

[3]  P. Holland,et al.  Discrete Multivariate Analysis. , 1976 .

[4]  R. Shapley,et al.  Broadband temporal stimuli decrease the integration time of neurons in cat striate cortex , 1992, Visual Neuroscience.

[5]  S. Amari Information Geometry on Hierarchical Decomposition of Stochastic Interactions , 2007 .

[6]  B J Richmond,et al.  Stochastic nature of precisely timed spike patterns in visual system neuronal responses. , 1999, Journal of neurophysiology.

[7]  Moshe Abeles,et al.  Corticonics: Neural Circuits of Cerebral Cortex , 1991 .

[8]  B J Richmond,et al.  Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. II. Quantification of response waveform. , 1987, Journal of neurophysiology.

[9]  Michael J. Berry,et al.  The Neural Code of the Retina , 1999, Neuron.

[10]  A. P. Georgopoulos,et al.  Variability and Correlated Noise in the Discharge of Neurons in Motor and Parietal Areas of the Primate Cortex , 1998, The Journal of Neuroscience.

[11]  Robert E. Kass,et al.  A Spike-Train Probability Model , 2001, Neural Computation.

[12]  Emery N. Brown,et al.  The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis , 2002, Neural Computation.

[13]  R N Lemon,et al.  Precise spatiotemporal repeating patterns in monkey primary and supplementary motor areas occur at chance levels. , 2000, Journal of neurophysiology.

[14]  J. Donoghue,et al.  Neuronal Interactions Improve Cortical Population Coding of Movement Direction , 1999, The Journal of Neuroscience.

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

[16]  John M. Beggs,et al.  Neuronal Avalanches in Neocortical Circuits , 2003, The Journal of Neuroscience.

[17]  William Bialek,et al.  Reading a Neural Code , 1991, NIPS.

[18]  William R. Softky,et al.  The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[19]  T. Sejnowski,et al.  Discovering Spike Patterns in Neuronal Responses , 2004, The Journal of Neuroscience.

[20]  Shun-ichi Amari,et al.  Information-Geometric Decomposition in Spike Analysis , 2001, NIPS.

[21]  R. Kass,et al.  Statistical analysis of temporal evolution in single-neuron firing rates. , 2002, Biostatistics.

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

[23]  J. Movshon,et al.  The statistical reliability of signals in single neurons in cat and monkey visual cortex , 1983, Vision Research.

[24]  Jr. Hall Combinatorial theory (2nd ed.) , 1998 .

[25]  B. Richmond,et al.  Coding strategies in monkey V1 and inferior temporal cortices. , 1998, Journal of neurophysiology.

[26]  Michael N. Shadlen,et al.  Noise, neural codes and cortical organization , 1994, Current Opinion in Neurobiology.

[27]  E. Vaadia,et al.  Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. , 1993, Journal of neurophysiology.

[28]  Yutaka Sakai,et al.  Synchronous Firing and Higher-Order Interactions in Neuron Pool , 2003, Neural Computation.

[29]  TJ Gawne,et al.  How independent are the messages carried by adjacent inferior temporal cortical neurons? , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[30]  Carlos D. Brody,et al.  Correlations Without Synchrony , 1999, Neural Computation.

[31]  F. Mechler,et al.  Temporal coding of contrast in primary visual cortex: when, what, and why. , 2001, Journal of neurophysiology.

[32]  Shun-ichi Amari,et al.  Information geometry on hierarchy of probability distributions , 2001, IEEE Trans. Inf. Theory.

[33]  A. Dean The variability of discharge of simple cells in the cat striate cortex , 2004, Experimental Brain Research.

[34]  E. Vaadia,et al.  Spatiotemporal structure of cortical activity: properties and behavioral relevance. , 1998, Journal of neurophysiology.

[35]  Matthew C Wiener,et al.  Decoding Spike Trains Instant by Instant Using Order Statistics and the Mixture-of-Poissons Model , 2003, The Journal of Neuroscience.

[36]  Shun-ichi Amari,et al.  Information-Geometric Measure for Neural Spikes , 2002, Neural Computation.

[37]  C. Stevens,et al.  Input synchrony and the irregular firing of cortical neurons , 1998, Nature Neuroscience.

[38]  A. Aertsen,et al.  Spike synchronization and rate modulation differentially involved in motor cortical function. , 1997, Science.

[39]  Jonathan D. Victor,et al.  Metric-space analysis of spike trains: theory, algorithms and application , 1998, q-bio/0309031.

[40]  J. N. R. Jeffers,et al.  Graphical Models in Applied Multivariate Statistics. , 1990 .