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Correlations and Coincidences: What's the difference, when does it matter, and how can we tell?

Jeff Beck

Computational Cognitive Neuroscience Laboratory, University of Rochester, USA

The number of possible states associated with a population of spiking neurons is intractably large. As such, any analysis of the neural code requires the use of simplifying assumptions to parameterize the joint distribution of stimuli and the neural responses. Estimations of information content and resulting conclusions about the neural code are both strongly affected by the choice of the parameterization and, when data is limited, by the subsequent parameter selection process.

This is a problem, not just for the neuroscientist, but for the brain as well. Fortunately, the brain seems to have solved this problem, and, in some cases, it seems to have solved it optimally. As such, it seems reasonable to investigate the neural operations that the brain utilizes to implement optimal inference in order to gain insight into the neural code. Here, we utilize the probabilistic population coding (PPC) framework to draw a natural link between neural statistics and neural operations. This framework is then used to demonstrate that the presence of stimulus dependent correlations/covariances does not, in itself, indicate that a non-linear population code is present. Rather, it is generally the case that one needs to know the stimulus dependence of the first 2*Nth moments to draw any conclusions about the information content of the Nth moment. Finally, we demonstrate the link between the PPC framework and Variational Bayesian logistic regression and argue that this is the proper tool to use when attempting to determine if a PPC is present that requires downstream neurons which implement non-linear operations such as coincidence detection.