Negative constant kernel

[arodland]

Considering that george supports the CosineKernel it probably can cope with negative covariances. My model instead uses an ExpSine2Kernel offset by a negative constant. But since ConstantKernel is parameterized by the log of the constant, it's impossible to specify a negative constant. I tried using -1 * ConstantKernel(abs_value) but that doesn't work either, probably since the * overload just constructs a ConstantKernel anyway.

[arodland]

arodland@dae7293 seems to work fine although I'm not sure if it's the best approach.

[stefanocovino]

Did you have any specific comment? I have exactly the same problem... :) essentially how to model processes with a (partially, at least) negative ACF.

Stefano

[arodland]

@stefanocovino my branch is working 100% fine for me. Just hoping for an opinion from @dfm .

[stefanocovino]

My first, naive, feeling is only that mathematically it could work, however by itself a negative kernel is probably not a kernel, at least according to Eq. 4.2 in Rasmussen and Williams. O course if you are just summing it to some other kernel what counts is the total sum that might well satisfy Eq. 4.2, possibly limiting the value of the constant. My 2 cents.

Bye,
Stefano

[arodland]

@stefanocovino yes, you're absolutely right, a negative constant is certainly not a kernel by that definition, but I don't care too much for terminological purity, and positive-semi-definiteness does get enforced on the final result when the solver tries to compute with it.