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Vrettas, Michail D.; Opper, Manfred; Cornford, Dan (2015)
Languages: English
Types: Article
Subjects:

Classified by OpenAIRE into

ACM Ref: MathematicsofComputing_NUMERICALANALYSIS
This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.
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    • Mid-points 1st interval Mid-points 2nd interval 1C. W. Gardiner, Handbook of Stochastic Methods: for physics, chemistry and the natural sciences, 3rd ed. (Springer Series in Synergetics, 2003).
    • 2A. Golightly and D. J. Wilkinson, Computational Statistics and Data analysis 52, 1674 (2007).
    • 3E. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability (Cambridge University Press, 2003).
    • 4M. Opper and D. Saad, eds., Advanced Mean Field Methods: Theory and Practice (MIT Press, Cambridge, MA, 2001).
    • 5F. J. Alexander, G. Eyink, and J. Restrepo, Journal of Statistical Physics 119, 1331 (2005).
    • 6P. Fearnhead, O. Papaspiliopoulos, and G. O. Roberts, Journal of the Royal Statistical Society 70, 755 (2008).
    • 7A. S. Paul and E. A. Wan, in Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. (2008) pp. 3621{3624.
    • 8Y. Tremolet, Quarterly Journal of the Royal Meteorological Society 132, 2483 (2006).
    • 9G. L. Eyink, J. M. Restrepo, and F. J. Alexander, Physica D: Nonlinear Phenomena 195, 347 (2004).
    • 10M. Gilorami and B. Calderhead, Journal of Royal Statistical Society - B 73, 123 (2011).
    • 11S. L. Cotter, G. O. Roberts, A. M. Stuart, and D. White, Statistical Science 28, 424 (2013).
    • 12S. Brooks, Handbook of Markov Chain Monte Carlo, 1st ed., edited by S. Brooks, A. Gelman, G. Jones, and X.-L. Meng, Handbooks of Modern Statistical Methods (Chapman and Hall / CRC, 2011).
    • 13J. C. Quin and H. D. I. Abarbanel, Journal of Computational Physics 230, 8168 (2011).
    • 14G. Evensen, Data assimilation: The Ensemble Kalman Filter, 2nd ed. (Springer, 2009).
    • 15P. J. van Leeuwen, Quarterly Journal of the Royal Meteorological Society 136, 1991 (2010).
    • 16F. Zhang, M. Zhang, and J. A. Hansen, Advances in Atmospheric Science 26, 1 (2009).
    • 17M. Zhang and F. Zhang, Monthly Weather Review 140, 587 (2012).
    • 18C. Archambeau, M. Opper, Y. Shen, D. Cornford, and J. ShaweTaylor, in Advances in Neural Information Processing Systems 20, edited by J. Platt, D. Koller, Y. Singer, and S. Roweis (2007) pp. 17{24.
    • 19M. D. Vrettas, D. Cornford, and M. Opper, Physica D: Nonlinear Phenomena 240, 1877 (2011).
    • 20R. P. Feynman, Statistical Mechanics: A Set Of Lectures, 2nd ed., Advanced Books Classics (Westview Press, 1998).
    • 21H. Kleinert, Path Integral in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets, 5th ed. (World Scienti c, 2009).
    • 22P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Di erential Equations, 3rd ed. (Springer, Applications of Mathematics, 1999).
    • 23C. Archambeau, D. Cornford, M. Opper, and J. Shawe-Taylor, Journal of Machine Learning Research (JMLR), Workshop and Conference Proceedings 1, 1 (2007).
    • 24A. Beskos, O. Papaspiliopoulos, G. O. Roberts, and P. Fearnhead, Journal of Royal Statistical Society 68, 333 (2006).
    • 25I. V. Girsanov, Theory of Probability and its Applications V, 285 (1960).
    • 26B. ksendal, Stochastic Di erential Equations, 5th ed., An Introduction with Applications (Springer-Verlag, 2005).
    • 27M. D. Vrettas, Approximate Bayesian techniques for inference in stochastic dynamical systems, Ph.D. thesis, Aston University, School of Engineering and Applied Science (2010).
    • 28M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, New York, 1964).
    • 29E. N. Lorenz, Journal of Atmospheric Science 20, 130 (1963).
    • 30E. N. Lorenz, Journal of Atmospheric Science 62, 1574 (2005).
    • 31E. N. Lorenz and K. Emanuel, Journal of Atmospheric Science 55, 399 (1998).
    • 32J. Simon and U. Je rey, IEEE Transaction on Automatic Control. 45, 477 (2000).
    • 33G. Parisi, Statistical Field Theory, Advanced Book Classics (Westview Press, 1998).
    • 34M. Opper and O. Winther, in Advances in Neural Information Processing Systems, Vol. 16, edited by S. Thrun, L. Saul, and B. Scholkopf (MIT Press, Cambridge, MA, 2004).
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