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Monday, July 20 • 8:00pm - 9:00pm
P180: Mean Field Theory Inference and Learning in Networks with Stochastic Natural Exponential Family Neurons

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Join Zoom Meeting: https://NTNU.zoom.us/j/68732806247?pwd=TXhONVNrdVZPbG9qbG9kMTgzdFNDUT09
Meeting ID: 687 3280 6247
Passcode: 858548

Ivan Davidovich
, Benjamin Dunn, John Hertz, Yasser Roudi

The advent of experimental techniques that allow for the simultaneous recording of an unprecedented number of neurons has created a necessity for analysis tools that can handle very large datasets. Non-equilibrium models from statistical mechanics such as the kinetic Ising model have established themselves as natural tools for studying these types of complex networks and datasets. The applicability of the kinetic Ising model is however limited by the binary nature of its neurons. To alleviate this constraint, we extend previous analyses based on statistical mechanics to dynamical models of networks in which the state of the neurons can take values according to distributions in the mono-parametric natural exponential family. Using a mean field approach, we obtain both dynamical TAP equations for the expected activity of these states when the connectivity of the network is known as well as a naive mean field estimation of the connectivity when the activity of the neurons has been observed. We test the validity and accuracy of our analytical results by applying them to simulations, obtaining good agreement within specific regions of parameter space. For the inference of the network's connectivity we compare to exact learning via gradient ascent, obtaining excellent agreement for networks of Gaussian neurons and small discrepancies for Poisson networks.

avatar for Ivan Davidovich

Ivan Davidovich

Postdoctoral Fellow, Kavli Institute for Systems Neuroscience, NTNU

Monday July 20, 2020 8:00pm - 9:00pm CEST
Slot 19