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A Scheme for Molecular Computation of Maximum Likelihood Estimators for Log-Linear Models

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DNA Computing and Molecular Programming (DNA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9818))

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Abstract

We propose a novel molecular computing scheme for statistical inference. We focus on the much-studied statistical inference problem of computing maximum likelihood estimators for log-linear models. Our scheme takes log-linear models to reaction systems, and the observed data to initial conditions, so that the corresponding equilibrium of each reaction system encodes the corresponding maximum likelihood estimator. The main idea is to exploit the coincidence between thermodynamic entropy and statistical entropy. We map a Maximum Entropy characterization of the maximum likelihood estimator onto a Maximum Entropy characterization of the equilibrium concentrations for the reaction system. This allows for an efficient encoding of the problem, and reveals that reaction networks are superbly suited to statistical inference tasks. Such a scheme may also provide a template to understanding how in vivo biochemical signaling pathways integrate extensive information about their environment and history.

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Notes

  1. 1.

    It is more common in statistics and statistical mechanics literature to write \(\theta _1 = \mathrm {e}^{-E_1}\) and \(\theta _2=\mathrm {e}^{-E_2}\) in terms of “energies” \(E_1, E_2\) so that \(P[X_2\mid E_1, E_2] \propto \mathrm {e}^{-E_1-E_2}\) for example.

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Acknowledgements

I thank Nick S. Jones, Anne Shiu, Abhishek Behera, Ezra Miller, Thomas Ouldridge, Gheorghe Craciun, and Bence Melykuti for useful discussions.

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Authors and Affiliations

  1. Tata Institute of Fundamental Research, Mumbai, 400 005, India

    Manoj Gopalkrishnan

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  1. Manoj Gopalkrishnan
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Correspondence to Manoj Gopalkrishnan .

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Editors and Affiliations

  1. ESPCI, Laboratoire Gulliver UMR 7083, Paris, France

    Yannick Rondelez

  2. Centre de Recherche Inria de Paris, Paris, France

    Damien Woods

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Gopalkrishnan, M. (2016). A Scheme for Molecular Computation of Maximum Likelihood Estimators for Log-Linear Models. In: Rondelez, Y., Woods, D. (eds) DNA Computing and Molecular Programming. DNA 2016. Lecture Notes in Computer Science(), vol 9818. Springer, Cham. https://doi.org/10.1007/978-3-319-43994-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-43994-5_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-43993-8

  • Online ISBN: 978-3-319-43994-5

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