ArticleJournal of the Royal Society, Interface2023
A reaction network scheme for hidden Markov model parameter learning.
Article in Journal of the Royal Society, Interface, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed.
- Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks.Journal of mathematical biology · 2025Article
- Deep Reinforcement Learning Data Collection for Bayesian Inference of Hidden Markov Models.IEEE transactions on artificial intelligence · 2025Article
- A reaction network scheme for hidden Markov model parameter learning.Journal of the Royal Society, Interface · 2023Article
- Probabilistic Inference with Polymerizing Biochemical Circuits.Entropy (Basel, Switzerland) · 2022Article
- On reaction network implementations of neural networks.Journal of the Royal Society, Interface · 2021Article
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Authors and funding
4 authors.
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Abstract
With a view towards artificial cells, molecular communication systems, molecular multiagent systems and federated learning, we propose a novel reaction network scheme (termed the Baum-Welch (BW) reaction network) that learns parameters for hidden Markov models (HMMs). All variables including inputs and outputs are encoded by separate species. Each reaction in the 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 positive fixed point of the BW algorithm for HMMs is a fixed point of the reaction network scheme, and vice versa. Furthermore, we prove that the 'expectation' step and the 'maximization' step of the reaction network separately converge exponentially fast and compute the same values as the E-step and the M-step of the BW algorithm. We simulate example sequences, and show that our reaction network learns the same parameters for the HMM as the BW algorithm, and that the log-likelihood increases continuously along the trajectory of the reaction network.
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