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dfm / araa-gps

Souce code for our ARA&A review of Gaussian process regression for astronomical time-series
MIT License
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Comparison of kernels - Figure 8 #22

Closed ericagol closed 1 year ago

ericagol commented 1 year ago

I'm curious what value of \gamma was inferred for the Rational quadratic kernel as this approaches the Squared Exponential kernel as \gamma -> \infty. I find it interesting that the Squared Exponential was so strongly preferred relative to the Matérn-3/2 given that these kernels look so similar. The squared-exponential kernel decreases more steeply at larger time separations, so I'm wondering if the better agreement of the squared exponential is caused by the late data predictions which are poorer in the case of the Matern-3/2 since that kernel would cause the predicted data to continue trending in the same direction?
It's also interesting that the Exponential Squared predicts a U-turn right at the end of the observed data - but maybe this is being drawn back by the mean? What if the mean value is allowed to vary? Would that give less preference for the squared exponential over Matern?

https://github.com/dfm/araa-gps/blob/a659c2ccdcbd30bacf6bb52e845f071ebae08a1f/src/tex/ms.tex#L707-L717

dfm commented 1 year ago

Here are the parameter inferences for the rational quadratic kernel:

for-eric

What if the mean value is allowed to vary? Would that give less preference for the squared exponential over Matern?

Good question! We didn't experiment with this, but I will say that our results were not really sensitive to the random seed or how we chose to leave out the data, so I don't think that it is just luck of the draw that the differences are so strong!

ericagol commented 1 year ago

@dfm Thanks for sharing that. I'm still unclear on why the differences in Bayesian evidence between the first two kernels and the third is so strong... and, FWIW, I think this would be good to understand this in order to give the reader a deeper intuition as to why these kernels can be distinguished. I still suspect that the reason the Bayesian evidence is so similar for squared exponential & rational quadratic is that the kernels are probably very similar.