A Swarm-Based Approach to Learning Phase-Type Distributions for Continuous Time Bayesian Networks

The use of phase-type distributions is an established method for extending the representational power of continuous time Bayesian networks beyond exponentially-distributed state transitions. In this paper, we propose a method for learning phase-type distributions from known parametric distributions. We find that by using particle swarm optimization to minimize a modified KL-divergence value, we are able to efficiently obtain good phase-type approximations for a variety of parametric distributions. Our experiments show that particle swarm optimization outperforms genetic algorithms and hill climbing with simulated annealing. In addition, we investigate the trade-off between accuracy and complexity with respect to the number of phases in the phase-type distribution. Finally, we propose and evaluate an extension that uses informed starting locations during optimization, which we found to improve convergence rates when compared to random initialization.