Kalman filtering and smoothing solutions to temporal Gaussian process regression models

  title={Kalman filtering and smoothing solutions to temporal Gaussian process regression models},
  author={Jouni Hartikainen and Simo Sarkka},
  journal={2010 IEEE International Workshop on Machine Learning for Signal Processing},
In this paper, we show how temporal (i.e., time-series) Gaussian process regression models in machine learning can be reformulated as linear-Gaussian state space models, which can be solved exactly with classical Kalman filtering theory. The result is an efficient non-parametric learning algorithm, whose computational complexity grows linearly with respect to number of observations. We show how the reformulation can be done for Matérn family of covariance functions analytically and for squared… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 12 references

Estimation with Applications to Tracking and Navigation

  • Y. Bar-Shalom, X. Li, T. Kirubarajan
  • Wiley Interscience,
  • 2001
1 Excerpt

Curve fitting and optimal design for prediction (with discussion)

  • A. O’Hagan
  • Journal of the Royal Statistical Society. Series…
  • 1978
2 Excerpts

Stochastic Processes and Filtering

  • A. H. Jazwinski
  • 1970

Maximum likelihood estimates of linear dynamic systems

  • H. E. Rauch, F. Tung, C. T. Striebel
  • AIAA Journal, vol. 3(8), pp. 1445–1450, 1965.
  • 1965
2 Excerpts

Stratonovich, Topics in the Theory of Random Noise

  • R L.
  • Gordon and Breach,
  • 1963
2 Excerpts

Spatial variation – stochastic models and their application to some problems in forest surveys and other sampling investigations

  • B. Matérn
  • Tech. Rep., Meddelanden från Statens…
  • 1960
1 Excerpt

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