# How to learn from a dataset of weighted polynomials

I have a dataset of weighted polynomials, i.e. each data point is a polynomial (of variable size/degree) together with a weight vector (of fixed size). Each data point has an integer label that ranges from 0 to 200. My question is: which ML algorithms can I use to try to learn the integer label associated to each (poly, weight) pair, considering len(poly) variable and len(weight) fixed? I tried a simple MLP only using the weights as features and achieved a $$R^2\approx65\%$$.

Edit: The (polynomials, weights) are solutions of a combinatorial system. They represent Calabi-Yau manifolds in a certain weighted projective space. It is worth mention that the polynomials are defined in 5 variables $$(x_0, \dots x_4)$$, and the length of coefficient vectors goes up to ~1000.

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• A polynomial ultimately is just a finite-length vector. How did you determine the coefficients and the weights?
– whuber
May 22 at 13:48
• Hey, @whuber. The (polynomials, weights) are solutions of a combinatorial system. They represent Calabi-Yau manifolds in a certain weighted projective space May 22 at 14:15
• Additionally, I think it is worth mention that the polynomials are defined in 5 variables (x_0, ..., x_4) , and the length of coefficient vectors goes up to ~1000 May 22 at 14:17
• Thank you, all that information is useful to know when thinking about your question. Please include it in the post itself so that readers with limited time will have what they need to think about this without having to scan through the comments (which sometimes can grow into very long threads or disappear altogether).
– whuber
May 22 at 16:54