Testing Noisy Low-Degree Polynomials for Sparsity

We consider the problem of testing if an unknown low-degree polynomial p over ℝn is sparse versus far from sparse, given access to noisy evaluations of the polynomial p at randomly chosen points. This is a natural property-testing version of various well-studied problems about learning low-degree sparse polynomials in the presence of noise, and is a generalization of the work of Chen, De, and Servedio (2020), on testing noisy linear functions for sparsity, to the more challenging setting of low-degree polynomials.