  Many applications of machine learning on discrete domains, such as learning
preference functions in recommender systems or auctions, can be reduced to
estimating a set function that is sparse in the Fourier domain. In this work,
we present a new family of algorithms for learning Fourier-sparse set
functions. They require at most $nk - k \log_2 k + k$ queries (set function
evaluations), under mild conditions on the Fourier coefficients, where $n$ is
the size of the ground set and $k$ the number of non-zero Fourier coefficients.
In contrast to other work that focused on the orthogonal Walsh-Hadamard
transform, our novel algorithms operate with recently introduced non-orthogonal
Fourier transforms that offer different notions of Fourier-sparsity. These
naturally arise when modeling, e.g., sets of items forming substitutes and
complements. We demonstrate effectiveness on several real-world applications.
