JUMP-Means: Small-Variance Asymptotics for Markov Jump Processes
This work addresses inference challenges in MJPs, which are used in domains like disease modeling and RNA folding, but it is incremental as it builds on existing small-variance asymptotics approaches.
The authors tackled the problem of degenerate trajectories and poor inference in Markov jump processes (MJPs) by applying small-variance asymptotics, resulting in JUMP-means algorithms that are competitive or outperform existing methods in speed and reconstruction accuracy.
Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance is poor in nonparametric models. We take a small-variance asymptotics (SVA) approach to overcome these limitations. We derive the small-variance asymptotics for parametric and nonparametric MJPs for both directly observed and hidden state models. In the parametric case we obtain a novel objective function which leads to non-degenerate trajectories. To derive the nonparametric version we introduce the gamma-gamma process, a novel extension to the gamma-exponential process. We propose algorithms for each of these formulations, which we call \emph{JUMP-means}. Our experiments demonstrate that JUMP-means is competitive with or outperforms widely used MJP inference approaches in terms of both speed and reconstruction accuracy.