JUMP-Means: Small-Variance Asymptotics for Markov Jump Processes
نویسندگان
چکیده
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 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.
منابع مشابه
Supplementary Material for Jump-means: Small-variance Asymptotics for Markov Jump Processes
To obtain the SVA objective from the parametric MJP model, we begin by scaling the exponential distribution f(t;λ) = λ exp(−λt), which is an exponential family distribution with natural parameter η = −λ, log-partition function ψ(η) = − ln(−η), and base measure ν(dt) = 1 [1]. To scale the distribution, introduce the new natural parameter η̃ = βη and log-partition function ψ̃(η̃) = βψ(η̃/β). The new ...
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