A reaction network scheme which implements inference and learning for Hidden Markov Models
This enables molecular communication and multi-agent systems to perform machine learning tasks, but it is an incremental adaptation of existing algorithms to a new domain.
The authors tackled the problem of implementing Hidden Markov Model (HMM) inference and learning in molecular systems by proposing the Chemical Baum-Welch Algorithm, a reaction network scheme that learns HMM parameters with fixed points matching the Baum-Welch algorithm and exponential convergence in simulation.
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.