| 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. |
- Roudi, Yasser, et al.
(författare)
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Multi-neuronal activity and functional connectivity in cell assemblies
- 2015
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Ingår i: Current Opinion in Neurobiology. - : Elsevier BV. - 0959-4388 .- 1873-6882. ; 32, s. 38-44
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Tidskriftsartikel (refereegranskat)abstract
- Our ability to collect large amounts of data from many cells has been paralleled by the development of powerful statistical models for extracting information from this data. Here we discuss how the activity of cell assemblies can be analyzed using these models, focusing on the generalized linear models and the maximum entropy models and describing a number of recent studies that employ these tools for analyzing multi-neuronal activity. We show results from simulations comparing inferred functional connectivity, pairwise correlations and the real synaptic connections in simulated networks demonstrating the power of statistical models in inferring functional connectivity. Further development of network reconstruction techniques based on statistical models should lead to more powerful methods of understanding functional anatomy of cell assemblies.
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