Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins

QC 20150625
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.

Hertz, JohnKTH,Stockholms universitet,Nordiska institutet för teoretisk fysik (Nordita),Niels Bohr Institute, Denmark,Nordic Institute for Theoretical Physics NORDITA(Swepub:kth)u1dyo9y9 (author)
Tyrcha, JoannaStockholms universitet,Matematiska institutionen(Swepub:su)joanna (author)
Roudi, YasserKTH,Stockholms universitet,Nordiska institutet för teoretisk fysik (Nordita),Kavli Institute for Systems Neuroscience/Centre for Neural Computation, Norway,Nordic Institute for Theoretical Physics NORDITA(Swepub:kth)u1uk5yod (author)
Stockholms universitetNordiska institutet för teoretisk fysik (Nordita) (creator_code:org_t)

By the author/editor: Battistin, Claud ...; Hertz, John; Tyrcha, Joanna; Roudi, Yasser

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NATURAL SCIENCES: NATURAL SCIENCES; and Physical Science ...; and Other Physics To ...

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