| 1. |
- Battistin, Claudia, et al.
(författare)
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Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins
- 2015
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Ingår i: Journal of Statistical Mechanics. - 1742-5468.
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 2. |
- Borysov, Stanislav, et al.
(författare)
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U.S. stock market interaction network as learned by the Boltzmann machine
- 2015
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Ingår i: European Physical Journal B. - : Springer Berlin/Heidelberg. - 1434-6028 .- 1434-6036. ; 88:12, s. 1-14
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Tidskriftsartikel (refereegranskat)abstract
- We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented results show that binarization preserves the correlation structure of the market. Properties of distributions of external fields and couplings as well as the market interaction network and industry sector clustering structure are studied for different historical dates and moving window sizes. We demonstrate that the observed positive heavy tail in distribution of couplings is related to the sparse clustering structure of the market. We also show that discrepancies between the model’s parameters might be used as a precursor of financial instabilities.
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| 3. |
- Dunn, Benjamin, et al.
(författare)
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Correlations and Functional Connections in a Population of Grid Cells
- 2015
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Ingår i: PloS Computational Biology. - : Public Library of Science (PLoS). - 1553-734X .- 1553-7358. ; 11:2
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Tidskriftsartikel (refereegranskat)abstract
- We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a maximum entropy kinetic pairwise model (kinetic Ising model), study their functional connectivity. Even when we account for the covariations in firing rates due to overlapping fields, both the pairwise correlations and functional connections decay as a function of the shortest distance between the vertices of the spatial firing pattern of pairs of grid cells, i.e. their phase difference. They take positive values between cells with nearby phases and approach zero or negative values for larger phase differences. We find similar results also when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs. The inferred connections between neurons in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections found between cells of the same module. Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of grid pattern.
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| 4. |
- Dunn, Benjamin, et al.
(författare)
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Learning and inference in a nonequilibrium Ising model with hidden nodes
- 2013
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755 .- 1550-2376. ; 87:2, s. 022127-
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Tidskriftsartikel (refereegranskat)abstract
- We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.
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| 5. |
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| 6. |
- Hertz, John A., et al.
(författare)
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Ising model for inferring network structure from spike data
- 2013
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Ingår i: Principle of Neural Coding. - Boca/Raton : CRC Press. - 9781439853306 - 9781439853313 ; , s. 527-546
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Bokkapitel (refereegranskat)abstract
- Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of a simple model network to make its spike trains resemble the data as much as possible. The connections in the model network can then give us an idea of how the real neurons that generated the data are connected and how they influence each other. In this chapter we describe how to do this for the simplest kind of model: an Ising network. We derive algorithms for finding the best model connection strengths for fitting a given data set, as well as faster approximate algorithms based on mean field theory. We test the performance of these algorithms on data from model networks and experiments.
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| 7. |
- Hertz, John A., et al.
(författare)
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Path integral methods for the dynamics of stochastic and disordered systems
- 2017
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Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 50:3
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Forskningsöversikt (refereegranskat)abstract
- We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose/Janssen-De Dominicis-Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.
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| 8. |
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| 9. |
- Hertz, John, et al.
(författare)
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Ising models for inferring network structure from spike data
- 2013
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Ingår i: Principles of Neural Coding. - : CRC Press. ; , s. 527-546
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Now that we can record the spike trains of large numbers of neurons simultaneously, we have a chance, for the first time in the history of neuroscience, to start to understand how networks of neurons work. But how are we to proceed, once we have such data? In this chapter, we will review some ideas we have been developing. The reader will recognize that we are only describing the very first steps in a long journey. But we hope that they will help point the way toward real progress some time in the not-too-distant future.
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| 10. |
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