Using batch-GP for learnign single common GP over multiple experiments

Howdy folks,

Reading the docs, I understand that batch-GP is meant to learn k independent GPs, from k independent labels y over a common data set x.

y1 = f1(x), y2 = f2(x), ..., yk = fk(x) , for k independent GPs.

But how would one go about using batch-GP to learn a single common GP, from k independent experiments of the same underlying process?

y1=f(x1), y2 = f(x2), ..., yk=f(xk) for one and the same GP

For instance, I have k sets of data and labels (y) representing measurements of how the temperature changes over altitude (x) (e.g. from weather balloons launched at k different geographical locations), and I want to induce a GP prior hat represents the temperature change over altitude between mean sea level and some maximum altitude, marginalized over the all geographical areas.

Thanks in advance

Galto

[jilsamia]

Hi, I also have the same issue, my input data has a dimension of N*10 and I want to have the same gaussian process for all the features. I used this tutorial as a reference https://docs.gpytorch.ai/en/v1.1.1/examples/06_PyTorch_NN_Integration_DKL/Deep_Kernel_Learning_DenseNet_CIFAR_Tutorial.html but they learn one GP for every feature. Anyone knows how to do that ? Thanks

[edebrouwer]

Any update regarding training a single GP on different datasets ?