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

Code

• github.com/chrislybaer/aaai-ssft
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• github.com/marketdesignresearch/FA_based_ICAs
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• github.com/marketdesignresearch/FA-based-ICAs
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Abstract

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 _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.

Tasks

Reproductions