Learning Set Functions that are Sparse in Non-Orthogonal Fourier Bases

Many applications of machine learning on discrete domains, such as preference functions in recommender systems or auctions, can be reduced to estimating a set function that is sparse the Fourier domain. In this work, we present new family algorithms for Fourier-sparse functions. They require at most nk − k log + queries (set evaluations), under mild conditions coefficients, where n size ground and number non-zero coefficients. contrast other work focused orthogonal Walsh-Hadamard transform (WHT), our novel operate with recently introduced non-orthogonal transforms offer different notions Fourier-sparsity. These naturally arise when modeling, e.g., sets items forming substitutes complements. We demonstrate effectiveness several real-world applications.