TY - JOUR

T1 - A reaction network scheme for hidden Markov model parameter learning

AU - Wiuf, Carsten

AU - Behera, Abhishek

AU - Singh, Abhinav

AU - Gopalkrishnan, Manoj

N1 - Publisher Copyright: © 2023 The Authors.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Baum-Welch algorithm

KW - hidden Markov model

KW - molecular programming

KW - statistical learning

KW - synthetic biology

UR - http://www.scopus.com/inward/record.url?scp=85163707636&partnerID=8YFLogxK

U2 - 10.1098/rsif.2022.0877

DO - 10.1098/rsif.2022.0877

M3 - Journal article

C2 - 37340782

AN - SCOPUS:85163707636

VL - 20

JO - Journal of the Royal Society Interface

JF - Journal of the Royal Society Interface

SN - 2042-8898

IS - 203

M1 - 20220877

ER -