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JUMP-Means: Small-Variance Asymptotics for Markov Jump Processes

Jonathan Huggins, Karthik Narasimhan, Ardavan Saeedi, Vikash Mansinghka
Proceedings of The 32nd International Conference on Machine Learning, pp. 693–701, 2015

Abstract

Markov jump processes (MJPs) are used to model a wide range of phenomenon from disease progression to RNA path folding. However, existing methods suffer from a number of shortcomings: degenerate trajectories in the case of ML estimation of parametric models and poor inferential performance in the case of 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 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.

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