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

TY - GEN

T1 - A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models

AU - Singh, Abhinav

AU - Wiuf, Carsten

AU - Behera, Abhishek

AU - Gopalkrishnan, Manoj

PY - 2019

Y1 - 2019

N2 - 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 “Expectation� step and the “Maximization� 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.

AB - 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 “Expectation� step and the “Maximization� 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.

UR - http://www.scopus.com/inward/record.url?scp=85070695913&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-26807-7_4

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

M3 - Article in proceedings

AN - SCOPUS:85070695913

SN - 9783030268060

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 54

EP - 79

BT - DNA Computing and Molecular Programming - 25th International Conference, DNA 25, Proceedings

A2 - Liu, Yan

A2 - Thachuk, Chris

PB - Springer

T2 - 25th International Conference on DNA Computing and Molecular Programming, DNA 2019

Y2 - 5 August 2019 through 9 August 2019

ER -