I have an observation that looks like the following
I wanted to extract the periodicity in the observation. So I used a sum of a periodic kernel, a linear kernel, and noise and performed Gaussian Process Regression. It resulted in a reasonable period. What I’m unable to interpret is the value of c, which is tightly constrained to 1. I regressed a similar observation and also found a value of c close to 1.
Can someone help me interpret the value of c, please?
That should be the offset hyperparameter of the linear kernel. The linear kernel is a bit different than other kernels, in that it is non-stationary, with the offset being the point in x through which all posterior functions pass through. https://www.cs.toronto.edu/~duvenaud/cookbook has a good overview of kernels and compositions of kernels. I find the linear kernel a bit strange to interpret, so if your case suggests a linearly decreasing trend you could also demean your data or express that relationship via a parametric linear mean function directly.