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distillpub / post--visual-exploration-gaussian-processes

A Visual Exploration of Gaussian Processes
http://distill.pub/2019/visual-exploration-gaussian-processes
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Dimension of kernels #59

Open mr-easy opened 4 years ago

mr-easy commented 4 years ago

I am a bit confused with the dimension of the kernel function.

k: R^n x R^n -> R Sigma = COV(X, X') = k(t, t')

What is n here? Are we having a 1-dimensional regression problem or n-dimensional? The covariance matrix should be nxn, while the kernel will give just a scalar real value?

Sorry for adding it as an issue. Can't find any way to comment.

And THANKS a lot for this great article, really helpful.

grtlr commented 4 years ago

Sorry for replying so late, for some reason this issue has slipped through.

The inputs to the kernel function can be high-dimensional vectors; its result will be a scalar value. The covariance matrix has as many rows and columns as there are samples in the dataset and the kernel function is evaluated for each pair in the matrix.

I hope this clears things up!