Hi
Let R be a binary relation between natural numbers.
I have an NP-complete algorithm that computes (exactly) what pairs belong to R, which works very well for small scopes but doesn't scale for higher scopes.
The following plot shows the pairs that belong to R up to scope 7.
What I want, is to extrapolate this pattern to higher scopes. However, I don't know what method to use.
Cons: I don't have as much data as is usually required to train a model (in the case the selected method requires it). In this particular case, I have only 21 pairs. Pros: It doesn't need to be perfect. Just an approximation is enough.
You might think that two linear regressions, one with the pairs at the top and the other with the pairs at the bottom are enough to resolve that the pairs in the middle belong to R. However, there are more complex patterns to extrapolate like the following ones:
