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Hopefully this question is not too simple or too general. I am working on a problem right now in which I am given different sets of data. Each data set consists of some number of samples (sampled at irregular points throughout the input space) which consist of a single output value that is associated with a specific number of input values. However, the number of input values varies across each data set (usually between 1 and 10, but possibly much larger).

To quickly illustrate:


Data Set 1:

sample1: (in0, in1, in2) -> out0

sample2: (in0, in1, in2) -> out1

...

sampleN: (in0, in1, in2) -> outN

Data Set 2:

sample1: (in0, in1, in2, in3, in4) -> out0

sample2: (in0, in1, in2, in3, in4) -> out1

...

sampleM: (in0, in1, in2, in3, in4) -> outM


My overall goal is to be able to use a single interpolation/regression technique for every data set regardless of the number of input dimensions. My only constraints are that the prediction technique must be able to scale to any number of dimensions without changing the underlying implementation, and that it must work for data that is not necessarily sampled with uniform spacing.

So far I have had some success using Nearest Neighbor and Radial Basis Functions for interpolation but I am by no means an expert on multidimensional interpolation techniques and was wondering if there were any other methods that might be suitable for this task.

Thanks!

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