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Gaussian Process Regression Networks

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  • Andrew Gordon Wilson
  • David A. Knowles
  • Zoubin Ghahramani
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    Abstract

    We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables, input dependent length-scales and amplitudes, and heavy-tailed predictive distributions. We derive both efficient Markov chain Monte Carlo and variational Bayes inference procedures for this model. We apply GPRN as a multiple output regression and multivariate volatility model, demonstrating substantially improved performance over eight popular multiple output (multi-task) Gaussian process models and three multivariate volatility models on benchmark datasets, including a 1000 dimensional gene expression dataset.

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    File URL: http://arxiv.org/pdf/1110.4411
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1110.4411.

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    Date of creation: Oct 2011
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    Handle: RePEc:arx:papers:1110.4411

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    Web page: http://arxiv.org/

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    1. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    3. Neil Shephard & Siddhartha Chib, 1999. "Analysis of High Dimensional Multivariate Stochastic Volatility Models," Economics Series Working Papers 1999-W18, University of Oxford, Department of Economics.
    4. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(1), pages 116-31, February.
    5. Brooks, Chris & Burke, Simon P. & Persand, Gita, 2001. "Benchmarks and the accuracy of GARCH model estimation," International Journal of Forecasting, Elsevier, Elsevier, vol. 17(1), pages 45-56.
    6. Joan Jasiak & R. Sufana & C. Gourieroux, 2005. "The Wishart Autoregressive Process of Multivariate Stochastic Volatility," Working Papers, York University, Department of Economics 2005_2, York University, Department of Economics.
    7. Alexandra M. Schmidt & Anthony O'Hagan, 2003. "Bayesian inference for non-stationary spatial covariance structure via spatial deformations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 743-758.
    8. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
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