# Sparse approximation of triangular transports on bounded domains

@article{Zech2020SparseAO, title={Sparse approximation of triangular transports on bounded domains}, author={Jakob Zech and Youssef M. Marzouk}, journal={ArXiv}, year={2020}, volume={abs/2006.06994} }

Let ρ and π be two probability measures on [−1, 1] with positive and analytic Lebesgue densities. We investigate the approximation of the unique triangular monotone (Knothe– Rosenblatt) transport T : [−1, 1] → [−1, 1], such that the pushforward T♯ρ equals π. It is shown that for d ∈ N there exist approximations T̃ of T based on either sparse polynomial expansions or ReLU networks, such that the distance between T̃♯ρ and π decreases exponentially. More precisely, we show error bounds of the type… CONTINUE READING

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