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Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins
Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Niels Bohr Institute, Denmark.
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Kavli Institute for Systems Neuroscience/Centre for Neural Computation, Norway.
Number of Authors: 4
2015 (English)In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, P05021Article in journal (Refereed) Published
Abstract [en]

We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief propagation (BP) and susceptibility propagation (SusP) can then be used to infer the states of hidden variables and to learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the Thouless-Anderson-Palmer (TAP) equations for reconstructing the connections.

Place, publisher, year, edition, pages
2015. P05021
Keyword [en]
cavity and replica method, disordered systems (theory), statistical inference, kinetic Ising models
National Category
Mechanical Engineering Mathematics
URN: urn:nbn:se:su:diva-119088DOI: 10.1088/1742-5468/2015/05/P05021ISI: 000355588600021OAI: diva2:843304
Available from: 2015-07-28 Created: 2015-07-27 Last updated: 2015-07-28Bibliographically approved

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Tyrcha, Joanna
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Nordic Institute for Theoretical Physics (Nordita)Department of Mathematics
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