Statistical Complexity of Neural Spike Trains

Abstract

We present closed-form expressions for the entropy rate, statistical complexity, and predictive information for the spike train of a single neuron in terms of the first passage time probability distribution. Our analysis applies to any one-dimensional neural model where observation of a spike causes the neuron to ``reset'' to some membrane voltage and in which any noise term is uncorrelated in time. We then use these formulae to study the linear leaky integrate-and- fire and quadratic integrate-and-fire neurons driven by white noise in the naturally spiking regime. The statistical complexity is simply related to the interspike interval's mean and coefficient of variation. The excess entropy, or the total predictive information, is highest for neural spike trains with low interspike interval coefficients of variation. Both the statistical complexity and the excess entropy arise naturally in the context of predictive rate-distortion and could be useful for characterizing ``predictor'' neurons that learn to predict other neurons.

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Document Details

Document Type
Technical Report
Publication Date
Aug 28, 2014
Accession Number
ADA618984

Entities

People

  • Jim Crutchfield
  • Michael R DeWeese
  • Sarah Marzen

Organizations

  • University of California

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Coefficients
  • Distortion
  • Distribution Functions
  • Equations
  • Excess Entropy
  • Information Operations
  • Intervals
  • Membranes
  • Military Research
  • Noise
  • Observation
  • Phase Transformations
  • Probability
  • Probability Distributions
  • White Noise

Readers

  • Approximation Theory.
  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Computational Modeling and Simulation