Gaussian Process Kernels for time series : one kernel for t<0 and one for t>0, is it possible?

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I have small time series, (t_i, Y_i)_{i<N} (N ~ 20 and varying from one to another). Now, I know that for some t_i <0 the behaviour is different than for t_i>0, and from one series to the other the index "i" that cuts the two processes time zone, is different. Well, it seems that I can cook a kernel for the time zone independently, but I was wandering that is it possible to glue both kernels?

I can use scikit-learn or numpyro or pytorch if you point me an example. Thanks

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