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Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Niels Bohr Institute, Copenhagen, Denmark.
2014 (English)In: Mathematical Biosciences and Engineering, ISSN 1547-1063, Vol. 11, no 1, 149-165 p.Article in journal (Refereed) Published
Abstract [en]

We derive learning rules for finding the connections between units in stochastic dynamical networks from the recorded history of a visible subset of the units. We consider two models. In both of them, the visible units are binary and stochastic. In one model the hidden units are continuous-valued, with sigmoidal activation functions, and in the other they are binary and stochastic like the visible ones. We derive exact learning rules for both cases. For the stochastic case, performing the exact calculation requires, in general, repeated summations over an number of configurations that grows exponentially with the size of the system and the data length, which is not feasible for large systems. We derive a mean field theory, based on a factorized ansatz for the distribution of hidden-unit states, which offers an attractive alternative for large systems. We present the results of some numerical calculations that illustrate key features of the two models and, for the stochastic case, the exact and approximate calculations.

Place, publisher, year, edition, pages
2014. Vol. 11, no 1, 149-165 p.
Keyword [en]
Network inference, latent variables, kinetic Ising models, mean field theory, hidden units
National Category
Mathematics Biological Sciences
URN: urn:nbn:se:su:diva-97633DOI: 10.3934/mbe.2014.11.149ISI: 000326979900011OAI: diva2:680881
10th International Workshop on Neural Coding (NC), SEP 02-07, 2012, Prague, CZECH REPUBLIC


Available from: 2013-12-18 Created: 2013-12-16 Last updated: 2013-12-18Bibliographically approved

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Tyrcha, JoannaHertz, John
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