2021/07/28 by Jakob Zech, Zech, Jakob, Youssef Marzouk +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2107.13422
openalex publication_date 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For two probability measures ρ and π on [-1,1]ℕ we investigate the approximation of the triangular Knothe-Rosenblatt transport T:[-1,1]ℕ→ [-1,1]ℕ 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 possible to efficiently approximately sample from certain high-dimensional measures by transforming a lower-dimensional latent variable.