Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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BCCN AG-Seminar

Tuesday, 26.01.2010 17 c.t.

Probabilistic Models of Neural Populations

by Prof. Dr. Matthias Bethge
from Computational Vision & Neuroscience Group, MPI for Biological Cybernetics, Tübingen

Contact person: Fred Wolf


Seminarraum Haus 2, 4. Stock (Bunsenstr.)


Sensory signals exhibit many degrees of freedom in space and time. The representation and processing of these signals cannot be done by individual neurons in isolation but requires a coordinated sharing of labor among large population of neurons. Probabilistic models of neural populations are thus an important tool to achieve a quantitative understanding of the collective information processing in the brain. One critical aspect of the coordination between different neurons is that the timing of action potentials in spiking neurons depends on the temporal dynamics of their inputs, and contains information about temporal fluctuations of a stimulus. Leaky integrate-and-fire neurons constitute a popular class of encoding models in which spike times depend directly on the temporal structure of their inputs. However, optimal decoding rules for these models have only been studied explicitly in the noiseless case. Here, we study decoding rules for probabilistic inference of a continuous stimulus from the spike times of a population of leaky integrate-and-fire neurons with noise threshold fluctuations. We derive three algorithms for approximating the posterior distribution over stimuli as a function of the observed spike trains. In addition to a reconstruction of the stimulus, we thus obtain an estimate of the uncertainty as well. Furthermore, we also derive a `spike-by-spike' online decoding scheme that recursively updates the posterior with the arrival of each new spike. We use these decoding rules to reconstruct time varying stimuli represented by a Gaussian process from spike trains of single neurons as well as neural populations.

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