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Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing.

ABSTRACT: Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes.

SUBMITTER: Xu J

PROVIDER: S-EPMC4775097 | biostudies-literature | 2015 Jul

REPOSITORIES: biostudies-literature

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Project description:Cardiac magnetic resonance (CMR) is a key tool for cardiac work-up. However, arrhythmia can be responsible for arrhythmia-related artifacts (ARA) and increased scan time using segmented sequences. The aim of this study is to evaluate the effect of cardiac arrhythmia on image quality in a comparison of a compressed sensing real-time (CSrt) cine sequence with the reference prospectively gated segmented balanced steady-state free precession (Cineref) technique regarding ARA. A total of 71 consecutive adult patients (41 males; mean age = 59.5 ± 20.1 years (95% CI: 54.7-64.2 years)) referred for CMR examination with concomitant irregular heart rate (defined by an RR interval coefficient of variation >10%) during scanning were prospectively enrolled. For each patient, two cine sequences were systematically acquired: first, the reference prospectively triggered multi-breath-hold Cineref sequence including a short-axis stack, one four-chamber slice, and a couple of two-chamber slices; second, an additional single breath-hold CSrt sequence providing the same slices as the reference technique. Two radiologists independently assessed ARA and image quality (overall, acquisition, and edge sharpness) for both techniques. The mean heart rate was 71.8 ± 19.0 (SD) beat per minute (bpm) (95% CI: 67.4-76.3 bpm) and its coefficient of variation was 25.0 ± 9.4 (SD) % (95% CI: 22.8-27.2%). Acquisition was significantly faster with CSrt than with Cineref (Cineref: 556.7 ± 145.4 (SD) s (95% CI: 496.7-616.7 s); CSrt: 23.9 ± 7.9 (SD) s (95% CI: 20.6-27.1 s); p < 0.0001). A total of 599 pairs of cine slices were evaluated (median: 8 (range: 6-14) slices per patient). The mean proportion of ARA-impaired slices per patient was 85.9 ± 22.7 (SD) % using Cineref, but this was figure was zero using CSrt (p < 0.0001). The European CMR registry artifact score was lower with CSrt (median: 1 (range: 0-5)) than with Cineref (median: 3 (range: 0-3); p < 0.0001). Subjective image quality was higher in CSrt than in Cineref (median: 3 (range: 1-3) versus 2 (range: 1-4), respectively; p < 0.0001). In line, edge sharpness was higher on CSrt cine than on Cineref images (0.054 ± 0.016 pixel-1 (95% CI: 0.050-0.057 pixel-1) versus 0.042 ± 0.022 pixel-1 (95% CI: 0.037-0.047 pixel-1), respectively; p = 0.0001). Compressed sensing real-time cine drastically reduces arrhythmia-related artifacts and thus improves cine image quality in patients with arrhythmia.

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Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing.

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