2023/11/09 by Bamdad Hosseini, Hosseini, Bamdad, Alexander Hsu +3 · 6 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #49Q22 #60B05 #62F15 #62G86 #Caveolin-1 and cellular processes #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Probability (math.PR) #Reservoir Engineering and Simulation Methods
paper · pdf · doi:10.48550/arxiv.2311.05672
openalex publication_date 2023/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of constrained optimal transport problems that describe block-triangular Monge maps that characterize conditional measures along with their Kantorovich relaxations. This generalizes the theory of optimal triangular transport to separable infinite-dimensional function spaces with general cost functions. We further tailor our results to the case of Bayesian inference problems and obtain regularity estimates on the conditioning maps from the prior to the posterior. Finally, we present numerical experiments that demonstrate the computational applicability of our theoretical results for amortized and likelihood-free inference of functional parameters.