A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models

Abhinav Singh; Carsten Wiuf; Abhishek Behera; Manoj Gopalkrishnan

doi:10.1007/978-3-030-26807-7_4

A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models

Abhinav Singh^*, Carsten Wiuf, Abhishek Behera, Manoj Gopalkrishnan

^*Corresponding author af dette arbejde

Institut for Matematiske Fag

2 Citationer (Scopus)

Abstract

With a view towards molecular communication systems and molecular multi-agent systems, we propose the Chemical Baum-Welch Algorithm, a novel reaction network scheme that learns parameters for Hidden Markov Models (HMMs). Each reaction in our scheme changes only one molecule of one species to one molecule of another. The reverse change is also accessible but via a different set of enzymes, in a design reminiscent of futile cycles in biochemical pathways. We show that every fixed point of the Baum-Welch algorithm for HMMs is a fixed point of our reaction network scheme, and every positive fixed point of our scheme is a fixed point of the Baum-Welch algorithm. We prove that the â€œExpectationâ€� step and the â€œMaximizationâ€� step of our reaction network separately converge exponentially fast. We simulate mass-action kinetics for our network on an example sequence, and show that it learns the same parameters for the HMM as the Baum-Welch algorithm.

Originalsprog	Engelsk
Titel	DNA Computing and Molecular Programming - 25th International Conference, DNA 25, Proceedings
Redaktører	Yan Liu, Chris Thachuk
Antal sider	26
Forlag	Springer
Publikationsdato	2019
Sider	54-79
ISBN (Trykt)	9783030268060
ISBN (Elektronisk)	9783030268077
DOI	https://doi.org/10.1007/978-3-030-26807-7_4
Status	Udgivet - 2019
Begivenhed	25th International Conference on DNA Computing and Molecular Programming, DNA 2019 - Seattle, USA Varighed: 5 aug. 2019 → 9 aug. 2019

Konference

Konference	25th International Conference on DNA Computing and Molecular Programming, DNA 2019
Land/Område	USA
By	Seattle
Periode	05/08/2019 → 09/08/2019
Sponsor	International Society of Nanoscale Science, Computing, and Engineering, Microsoft Research (USA), National Science Foundation (USA), University of Washington

Navn	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Vol/bind	11648 LNCS
ISSN	0302-9743

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10.1007/978-3-030-26807-7_4

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Citationsformater

Singh, A., Wiuf, C., Behera, A., & Gopalkrishnan, M. (2019). A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models. I Y. Liu, & C. Thachuk (red.), DNA Computing and Molecular Programming - 25th International Conference, DNA 25, Proceedings (s. 54-79). Springer. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Bind 11648 LNCS https://doi.org/10.1007/978-3-030-26807-7_4

A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models. / Singh, Abhinav; Wiuf, Carsten; Behera, Abhishek et al.

DNA Computing and Molecular Programming - 25th International Conference, DNA 25, Proceedings. red. / Yan Liu; Chris Thachuk. Springer, 2019. s. 54-79 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 11648 LNCS).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

Singh, A, Wiuf, C, Behera, A & Gopalkrishnan, M 2019, A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models. i Y Liu & C Thachuk (red), DNA Computing and Molecular Programming - 25th International Conference, DNA 25, Proceedings. Springer, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), bind 11648 LNCS, s. 54-79, 25th International Conference on DNA Computing and Molecular Programming, DNA 2019, Seattle, USA, 05/08/2019. https://doi.org/10.1007/978-3-030-26807-7_4

Singh A, Wiuf C, Behera A, Gopalkrishnan M. A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models. I Liu Y, Thachuk C, red., DNA Computing and Molecular Programming - 25th International Conference, DNA 25, Proceedings. Springer. 2019. s. 54-79. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 11648 LNCS). doi: 10.1007/978-3-030-26807-7_4

Singh, Abhinav ; Wiuf, Carsten ; Behera, Abhishek et al. / A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models. DNA Computing and Molecular Programming - 25th International Conference, DNA 25, Proceedings. red. / Yan Liu ; Chris Thachuk. Springer, 2019. s. 54-79 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 11648 LNCS).

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A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models

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