A reaction network scheme which implements inference and learning for Hidden Markov Models
Abstract
With a view towards molecular communication systems and molecular multiagent systems, we propose the Chemical BaumWelch 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 BaumWelch 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 BaumWelch algorithm. We prove that the "Expectation" step and the "Maximization" step of our reaction network separately converge exponentially fast. We simulate massaction kinetics for our network on an example sequence, and show that it learns the same parameters for the HMM as the BaumWelch algorithm.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.09410
 Bibcode:
 2019arXiv190609410S
 Keywords:

 Computer Science  Emerging Technologies;
 Computer Science  Machine Learning;
 Quantitative Biology  Molecular Networks
 EPrint:
 Accepted at 25th International Conference on DNA Computing and Molecular Programming