Predict values of some numerical vectors by using other numerical vectors with all these vectors in the same vector set

StackOverflow https://stackoverflow.com/questions/22108800

Question

I need to solve a problem about predicting values of some numerical vectors by using other numerical vectors with all these vectors in the same vector set, which is generated by one or more black box functions.

Given a vector space:

P =[S_1, S_2, …, S_T |  Sk is a vector of q numbers, k = 1, ..., T] 

Find a sub-group of vectors g = {S_d | d belongs to 1, …, T } and a function h( S_d )

Such that

       Difference between the value of h(S_g) and S_r is minimized

       set g  + set r  =  set P 

       set g and set r have no overlap 

What kinds of knowledge I need to solve the problem ?

If the question should not be here, please tell me where it should be posted ?


update:

The question can be expressed as:

Given a set S of vectors, find a function h() whose arguments are from part of vectors of S (we call it S1). The output of h() are the vectors of another part of S (we call it S2). The output h() are the predicated values for S2. We need to keep the prediction errors minimized and the size of S1 minimal.

How to find the h() ?

No correct solution

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