Network inference with hidden units
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''...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.149 |
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| author | Joanna Tyrcha John Hertz |
| author_facet | Joanna Tyrcha John Hertz |
| author_sort | Joanna Tyrcha |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-47dba400fd6644d4a0a6f9788993593a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-47dba400fd6644d4a0a6f9788993593a2025-01-24T02:26:48ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-08-0111114916510.3934/mbe.2014.11.149Network inference with hidden unitsJoanna Tyrcha0John Hertz1Department of Mathematics, Stockholm University, Kräftriket, S-106 91 StockholmNordita, Stockholm University and KTH, Roslagstullsbacken 23, S-106 91 StockholmWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.149mean field theoryhidden units.network inferencekinetic ising modelslatent variables |
| spellingShingle | Joanna Tyrcha John Hertz Network inference with hidden units Mathematical Biosciences and Engineering mean field theory hidden units. network inference kinetic ising models latent variables |
| title | Network inference with hidden units |
| title_full | Network inference with hidden units |
| title_fullStr | Network inference with hidden units |
| title_full_unstemmed | Network inference with hidden units |
| title_short | Network inference with hidden units |
| title_sort | network inference with hidden units |
| topic | mean field theory hidden units. network inference kinetic ising models latent variables |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.149 |
| work_keys_str_mv | AT joannatyrcha networkinferencewithhiddenunits AT johnhertz networkinferencewithhiddenunits |