Corpus ID: 236469372

Sparse approximation of triangular transports. Part II: the infinite dimensional case

@article{Zech2021SparseAO,
  title={Sparse approximation of triangular transports. Part II: the infinite dimensional case},
  author={Jakob Zech and Youssef M. Marzouk},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.13422}
}
For two probability measures ρ and π on [−1, 1] we investigate the approximation of the triangular Knothe–Rosenblatt transport T : [−1, 1] → [−1, 1] that pushes forward ρ to π. Under suitable assumptions, we show that T can be approximated by rational functions without suffering from the curse of dimension. Our results are applicable to posterior measures arising in certain inference problems where the unknown belongs to an (infinite dimensional) Banach space. In particular, we show that it is… Expand

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