May 31 and June 7, Simon Schultz will present two papers, introducing
the problem and sketching out the fundamental mathematical techniques
the first week, and then going through the results in the second.
A theoretical model of neuronal population coding of stimuli with both
continuous and discrete dimensions
Valeria Del Prete, Alessandro Treves, 2001, cond-mat/0103286
(submitted to Physical Review E).
In a recent study the initial rise of the mutual information between
the firing rates of N neurons and a set of p discrete stimuli has been
analytically evaluated, under the assumption that neurons fire
independently of one another to each stimulus and that each
conditional distribution of firing rates is gaussian. Yet real stimuli
or behavioural correlates are high-dimensional, with both discrete and
continuously varying features.Moreover, the gaussian approximation
implies negative firing rates, which is biologically
implausible. Here, we generalize the analysis to the case where the
stimulus or behavioural correlate has both a discrete and a continuous
dimension. In the case of large noise we evaluate the mutual
information up to the quadratic approximation as a function of
population size. Then we consider a more realistic distribution of
firing rates, truncated at zero, and we prove that the resulting
correction, with respect to the gaussian firing rates, can be
expressed simply as a renormalization of the noise parameter. Finally,
we demonstrate the effect of averaging the distribution across the
discrete dimension, evaluating the mutual information only with
respect to the continuously varying correlate.
ps.gz here.
Representational Accuracy of Stochastic Neural Populations
Stefan D. Wilke and Christian W. Eurich, Neural Computation, 2001. In press.
Fisher information is used to analyze the accuracy with which a neural
population encodes D stimulus features. It turns out that the form of
response variability has a major impact on the encoding capacity and
therefore plays an important role in the selection of an appropriate
neural model. In particular, in the presence of baseline firing, the
reconstruction error rapidly increases with D in the case of
Poissonian noise, but not for additive noise. The existence of
limited-range correlations of the type found in cortical tissue yields
a saturation of the Fisher information content as a function of the
population size only for an additive noise model. We also show that
random variability in the correlation coefficient within a neural
population, as found empirically, considerably improves the average
encoding quality. Finally, the representational accuracy of
populations with inhomogeneous tuning properties, either with
variability in the tuning widths or fragmented into specialized
subpopulations, is superior to the case of identical and radially
symmetric tuning curves usually considered in the literature.