nips nips2007 nips2007-214 nips2007-214-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Manfred Opper, Guido Sanguinetti
Abstract: Markov jump processes play an important role in a large number of application domains. However, realistic systems are analytically intractable and they have traditionally been analysed using simulation based techniques, which do not provide a framework for statistical inference. We propose a mean field approximation to perform posterior inference and parameter estimation. The approximation allows a practical solution to the inference problem, while still retaining a good degree of accuracy. We illustrate our approach on two biologically motivated systems.
[1] Harley H. McAdams and Adam Arkin. Stochastic mechanisms in gene expression. Proceedings of the National Academy of Sciences USA, 94:814–819, 1997.
[2] Long Cai, Nir Friedman, and X. Sunney Xie. Stochastic protein expression in individual cells at the single molecule level. Nature, 440:580–586, 2006.
[3] Yoshito Masamizu, Toshiyuki Ohtsuka, Yoshiki Takashima, Hiroki Nagahara, Yoshiko Takenaka, Kenichi Yoshikawa, Hitoshi Okamura, and Ryoichiro Kageyama. Real-time imaging of the somite segmentation clock: revelation of unstable oscillators in the individual presomitic mesoderm cells. Proceedings of the National Academy of Sciences USA, 103:1313–1318, 2006.
[4] Daniel T. Gillespie. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, 81(25):2340–2361, 1977.
[5] Eric Mjolsness and Guy Yosiphon. Stochastic process semantics for dynamical grammars. to appear in Annals of Mathematics and Artificial Intelligence, 2006.
[6] Richard J. Boys, Darren J. Wilkinson, and Thomas B. L. Kirkwood. Bayesian inference for a discretely observed stochastic kinetic model. available from http://www.staff.ncl.ac.uk/d.j.wilkinson/pub.html, 2004.
[7] Manfred Opper and David Saad (editors). Advanced Mean Field Methods. MIT press, Cambridge,MA, 2001.
[8] Cedric Archambeau, Dan Cornford, Manfred Opper, and John Shawe-Taylor. Gaussian process approximations of stochastic differential equations. Journal of Machine Learning Research Workshop and Conference Proceedings, 1(1):1–16, 2007.
[9] Manfred Opper and David Haussler. Bounds for predictive errors in the statistical mechanics of supervised learning. Physical Review Letters, 75:3772–3775, 1995.
[10] Uri Alon. An introduction to systems biology. Chapman and Hall, London, 2006.
[11] Andrew Golightly and Darren J. Wilkinson. Bayesian inference for stochastic kinetic models using a diffusion approximation. Biometrics, 61(3):781–788, 2005. 8