Is there a way to model, or represent/transform, a State-Space model as a Gaussian Process?
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asked May 17, 2021 at 10:17
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$\begingroup$ The answer is yes if the (Contibous-Time) State Space is linear and if it involves Gaussian noise(s). One simply derive the covariance kernel. However the converse is not true beause some GP can have long memory. It is very interesting to represent a GP in State-Space form but I can not see the point at doing the opposite. Is this really what is wanted? $\endgroup$– YvesCommented May 18, 2021 at 11:50
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$\begingroup$ @Yves, and how would one derive the covariance kernel? Do you have any references? $\endgroup$– An old man in the sea.Commented May 18, 2021 at 12:55
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1$\begingroup$ You will find good material provided by Simo Särkkä on State-Space Representation of Gaussian Process near slide #17. This (Finnish) source is closely related to that linked in the answer of @Chango. Since the state equation is a (Continuous time) autoregression, the covariance kernel of the vector state process can be given in a closed form involving exponential of matrices. $\endgroup$– YvesCommented May 18, 2021 at 14:16
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Yes there is for certain covariance functions the relationship is exact.
