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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., 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.

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., QC 20131217

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., AuthorCount:2

In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, using local averaging and thresholding. This transformation introduces parameters, which must be varied to characterize the behaviour of the system. The approach is illustrated on financial data, using three inference methods-equilibrium, synchronous and asynchronous inference-to construct functional connections between stocks. We show that the traded volume information is enough to obtain well-known results about financial markets that use, however, presumably richer price information: collective behaviour ('market mode') and strong interactions within industry sectors. Synchronous and asynchronous Ising inference methods give results that are coherent with equilibrium ones and are more detailed since the obtained interaction networks are directed.

In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, using local averaging and thresholding. This transformation introduces parameters, which must be varied to characterize the behaviour of the system. The approach is illustrated on financial data, using three inference methods-equilibrium, synchronous and asynchronous inference-to construct functional connections between stocks. We show that the traded volume information is enough to obtain well-known results about financial markets that use, however, presumably richer price information: collective behaviour ('market mode') and strong interactions within industry sectors. Synchronous and asynchronous Ising inference methods give results that are coherent with equilibrium ones and are more detailed since the obtained interaction networks are directed.

In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, using local averaging and thresholding. This transformation introduces parameters, which must be varied to characterize the behaviour of the system. The approach is illustrated on financial data, using three inference methods-equilibrium, synchronous and asynchronous inference-to construct functional connections between stocks. We show that the traded volume information is enough to obtain well-known results about financial markets that use, however, presumably richer price information: collective behaviour ('market mode') and strong interactions within industry sectors. Synchronous and asynchronous Ising inference methods give results that are coherent with equilibrium ones and are more detailed since the obtained interaction networks are directed.

In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, using local averaging and thresholding. This transformation introduces parameters, which must be varied to characterize the behaviour of the system. The approach is illustrated on financial data, using three inference methods-equilibrium, synchronous and asynchronous inference-to construct functional connections between stocks. We show that the traded volume information is enough to obtain well-known results about financial markets that use, however, presumably richer price information: collective behaviour ('market mode') and strong interactions within industry sectors. Synchronous and asynchronous Ising inference methods give results that are coherent with equilibrium ones and are more detailed since the obtained interaction networks are directed.