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I am trying to forecast various time-series with Gaussian Processes, using the functional approach like in the Mauna Loa example in section 5.4.3 of "Gaussian Processes for Machine Learning". (X = time, y = observed value at time-point).
Except for that particular example, I almost always end up with the forecast being the mean of the training data. Despite using a Periodic Kernel and setting the periodicity to 7 for a clear weekly pattern, the forecast stays flat and the fitted values for the training set are also close to the mean with almost no variation. With some manual grid search, I get the training data fit to match the training data better but the forecast stays flat again most of the time.

I have experimented with lots of different kernels (RBF, Periodic, etc.) and combinations, tried different starting points for the hyperparameters (especially variances and length-scales), used different time-scales and different scaling techniques for the observations (subtracting mean, dividing by std, both, no scaling at all). However, the forecasts are almost always flat.
Now I know that the kernel and hyperparameter choices should be reasonable but I don't think that it should be that hard to get meaningful output and that I am rather doing something wrong here.

The packages I tried are gpflow and sklearn on Python 3.6 and the parameters are being optimized via the marginal likelihood (no sparse GP or variational approximation)

My question is: Has anyone an idea what I could be doing wrong here or how to make it easier to get reasonable forecasts?

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  • $\begingroup$ were you able to find out what the issue was? $\endgroup$ – jaranda Mar 24 at 19:49
  • $\begingroup$ I resolved this more or less via trial-and-error. gaussianprocess.org/gpml/chapters/RW.pdf mention that Gaussian Process Regression can get stuck in local optima so I could imagine that this was the reason. $\endgroup$ – Sarem Seitz Sep 12 at 12:09

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