Subsampling under distributional constraints

Some complex models are frequently employed to describe physical and mechanical phenomena. In this setting we have an input X in a general space, and an output Y = f(X) where f is a very complicated function, whose computational cost for every new input is very high. We are given two sets of observations of X, S 1 and S 2 of different sizes such that only f(S 1 ) is available. We tackle the problem of selecting a subset S 3 ⊂ S 2 of smaller size on which to run the complex mode f , and such that the empirical distribution of f(S 3 ) is close to that of f(S 1 ) . We suggest three algorithms to solve this problem and show their efficiency using simulated datasets and the Airfoil self-noise data set.