Approximating Measures on Function Spaces: Transport and Truncation

arXiv:2609.17802 · math.PR, cs.NA, math.NA, stat.ML · Submitted 2026-09-15 · Read on arXiv

math.PR, cs.NA, math.NA, stat.ML

Submitted: 2026-09-15

Updated: 2026-09-15

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 31× in this paper · explained in 2 episodes
• Optimal Transport — 27× in this paper · explained in 5 episodes
• Generative Model — 24× in this paper · explained in 2 episodes
• Inverse Problem — 13× in this paper · explained in 2 episodes
• Generative Modeling — 12× in this paper · explained in 3 episodes
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Wasserstein Distance — 10× in this paper · explained in 4 episodes
• Flow Matching — 8× in this paper · explained in 8 episodes
• Generative Models — 7× in this paper · explained in 2 episodes
• Bayesian Inference — 6× in this paper · explained in 5 episodes
• Normalizing Flow — 6× in this paper · explained in 3 episodes
• Normalizing Flows — 5× in this paper · explained in 4 episodes
• Uncertainty Quantification — 5× in this paper · explained in 8 episodes
• Diffusion Model — 4× in this paper · explained in 8 episodes
• Diffusion Models — 4× in this paper · explained in 6 episodes
• Adaptation — 2× in this paper · explained in 1 episode
• Ambient Dimension — 2× in this paper · explained in 1 episode
• Consistency — 2× in this paper · explained in 3 episodes
• Flow Matching Model — 2× in this paper · explained in 2 episodes
• Simulation-based Inference — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Calibration — 1× in this paper · explained in 7 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Diffusion Process — 1× in this paper · explained in 2 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Domain Adaptation — 1× in this paper · explained in 5 episodes
• Empirical Coverage — 1× in this paper · explained in 2 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Optimal Transport (OT) — 1× in this paper · explained in 4 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 1× in this paper · explained in 3 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Transfer Learning — 1× in this paper · explained in 10 episodes

Sources

• Knothe-Rosenblatt maps via soft-constrained optimal transport
• BlackJAX: Composable Bayesian inference in JAX
• Optimal low-rank posterior covariance approximation in linear Gaussian inverse problems on Hilbert spaces
• Single-seed generation of Brownian paths and integrals for adaptive and high order SDE solvers
• Minimax Rates of Estimation for Optimal Transport Map between Infinite-Dimensional Spaces
• A friendly introduction to triangular transport
• Gaussian Optimal Transport Beyond Brenier's Theorem
• Functional normalizing flow for statistical inverse problems of partial differential equations

Related papers

• Sharp Deviations Bounds for Dirichlet Weighted Sums with Application to analysis of Bayesian algorithms
• Local Anticoncentration for Gaussian Boson Sampling via Conditional Wishart Geometry
• Beyond the Semicircle: Free Diffusion Models with Prescribed Equilibria
• A New Bound on the Cumulant Generating Function of Dirichlet Processes
• The Site Frequency Spectrum in an Exponentially Growing Population with Selection
• Statistical inference for a multiscale stochastic model of enzyme kinetics via propagation of chaos