Corpus ID: 219636243

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}
}
  • Jakob Zech, Youssef M. Marzouk
  • Published 2020
  • Mathematics, Computer Science
  • ArXiv
  • 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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