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- W2108013602 abstract "Let f : {-1, 1}n - ℝ be a polynomial with at most s non-zero real coefficients. We give an algorithm for exactly reconstructing f given random examples from the uniform distribution on {- 1,1}n that runs in time polynomial in n and 2s and succeeds if the function satisfies the unique sign property: there is one output value which corresponds to a unique set of values of the participating parities. This sufficient condition is satisfied when every coefficient of f is perturbed by a small random noise, or satisfied with high probability when s parity functions are chosen randomly or when all the coefficients are positive. Learning sparse polynomials over the Boolean domain in time polynomial in n and 2s is considered notoriously hard in the worst-case. Our result shows that the problem is tractable for almost all sparse polynomials.Then, we show an application of this result to hypergraph sketching which is the problem of learning a sparse (both in the number of hyperedges and the size of the hyperedges) hypergraph from uniformly drawn random cuts. We also provide experimental results on a real world dataset." @default.
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- W2108013602 date "2014-12-08" @default.
- W2108013602 modified "2023-09-24" @default.
- W2108013602 title "Sparse Polynomial Learning and Graph Sketching" @default.
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