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I am also very interested in knowing what to do when the dimension of the input space can vary. For example, suppose that I'm interested in learning 4-body gra

I am also very interested in knowing what to do when the dimension of the input space can vary. For example, suppose that I'm interested in learning 4-body gravitational motion using 3-body training data ie. predict total energy of a system given mutual distances. Notwithstanding the fact that this is trivial to compute directly, how do I set this up as a GP? Are there general strategies for this? What do I look up on google scholar, or what application field of ML most deals with this? Thanks a lot for your help.

Xcelerate 11y ago
> I am also very interested in knowing what to do when the dimension of the input space can vary. It is frequently the case that one's data lies on a (curvy) low dimensional manifold embedded within a higher dimensional space. Because of this, performing an orthogonal projection to a lower dimension is often a bad idea. Consider the famous "Swiss roll" dataset: http://www.convexoptimization.com/dattorro/manifold_learning.html http://www.convexoptimization.com/dattorro/manifold_learning... Although the data lies on a 2D manifold, there exists no affine subspace to project the data onto; one must instead perform a non-linear mapping. Problems like this are tackled using a variety of methods that attempt to "unroll" the manifold into its own vector space. The rest of the problem can then be solved using the tools of linear algebra. See http://repository.upenn.edu/cgi/viewcontent.cgi?article=1001&context=cis_papers http://repository.upenn.edu/cgi/viewcontent.cgi?article=1001... for example.