Friday evening, Poster II-75
Cosyne 2007
Distance Measure in Probability Space and Correct Measure of Variability
Kukjin Kang. RIKEN, BSI, Wako, Saitama, Japan.
In many experiments, spike times are recorded under several different conditions and the major
goal of the experiments is to describe the statistical difference between the spike sequences under
different experimental conditions such as different sensory stimuli. For a stationary Poisson
Process, the firing rates would measure the statistical difference of spike sequences reasonably.
However, non-Poissonian feastures as well as non-stationarity of spike sequence may make this
measure of the statistical difference very wrong. Statistical features of spike sequences from a real
neuron is not easy to be reproduced by a simple model. For example, Shinomoto et. al. found that a
simple LIF neuron or Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons
in prefrontal cortex. The inconsistency between the model and the data was mainly due to large
skewness values of the data which may be caused by anomalous long intervals embedded in spike
sequences. An important question is whether the statistical features that we fail to reproduce is
significant in terms of information within spike times.
Here we study how the error of discrimination based on spike times depends on higher order
moments of the ISI distribution than first two moments: mean and variance. We calculated
Chernoff distance for spike sequences generated by two different renewal processes where the
probabilities of generating spike sequences are determined by ISI distributions. Chernoff distance
measures the discrimination capability between a pair of distributions and has an exponential
relation with maximum-likelihood discrimination error in small-error limit. We consider a pair of
ISI distributions with the same coefficient of variability (CV) and different means. Then, Chernoff
distance between the corresponding distributions of spike sequences is calculated. We do this for
several analytical models such as gamma, inverse Gaussian (IG) and exponential with absolute
refractoriness period (ER) ISI distributions and ISI distribution of LIF neuron. We found that high
variability in terms of CV does not necessarily mean low information in spike times. This means
that the information within spike times strongly depends on higher moment than the mean and the
variance. This explains why Manwani et. al. found that the estimation error based on spike times is
not necessarily bigger with spike sequences with larger CV. Refractory period is very important for
spike sequences to have large discrimination capability. Spike sequences from LIF neuron are more
informative than that of IG and gamma distribution renewal processes when stationary voltage
level is close to threshold value. We also discuss the error of assuming Poisson distribution in
estimating discrimination capability based on spike times.
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