About mSigma (variance) in gaussian_process.cpp

[timberjack]

Dear Authors,

I am studying about gaussian process in LCB (Lower Confidence Bounds) evaluation. I take bo_branin.cpp as an example. I found variance is constantly lower than 1, which could be much smaller than mean value even in the early training step (for example, a gaussian model with only 2 samples trained. I tried my own example with mean value at around 170, but 0.2 variance with only 2 samples trained, where (170+-0.2) cannot contain the real value).

Through studying gaussian_process.cpp, I found that mSigma hugely decides the value of covariance. mSigma is set or gotten from function setHyperParameters and getHyperParameters in kernelRegressor.hpp, and is updated through kOptimizer in posterior_empirical.cpp. An initial 2-dimension points, mean and variance is combined into a 4-dimension vector to insert to kOptimizer. However, I doubt mean and variance is not calculated correctly as they are probably treated as same as the coordinates of 2-dimension points in kernelRegressor.hpp.

Could you help check about the calculation of variance? I feel interested into studying more.

Thanks,
Xianan

[rmcantin]

The variance is computed correctly. For certain models (not in all of them), the variance is estimated as a hyperparameter of the GP, like the kernel hyperparameters.