A machine learning framework for geodesics under spherical Wasserstein-Fisher-Rao metric and its application for weighted sample generation

DOI10.1007/s10915-023-02396-yzbMath1529.49025arXiv2208.12145OpenAlexW4388910882MaRDI QIDQ6184267

Jian-feng Lu, Yang Jing, Jiaheng Chen, Lei Li

Publication date: 5 January 2024

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.12145

zbMATH Keywords

Kullback-Leibler divergenceBayesian inferenceWasserstein distancesunbalanced optimal transportweighted samplesnormalizing flows

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Bayesian inference (62F15) Optimal transportation (49Q22)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computational Optimal Transport: With Applications to Data Science
• Density estimation by dual ascent of the log-likelihood
• A new optimal transport distance on the space of finite Radon measures
• Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures
• An interpolating distance between optimal transport and Fisher-Rao metrics
• Unbalanced optimal transport: dynamic and Kantorovich formulations
• Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures
• A parallel method for earth mover's distance
• The earth mover's distance as a metric for image retrieval
• Ensemble Kalman filter based sequential Monte Carlo sampler for sequential Bayesian inference
• Computational mean-field information dynamics associated with reaction-diffusion equations
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Sampling the posterior: an approach to non-Gaussian data assimilation
• The Variational Formulation of the Fokker--Planck Equation
• A survey of some recent applications of optimal transport methods to econometrics
• On Optimal Transport of Matrix-Valued Measures
• An Introduction to Variational Autoencoders
• Equation of State Calculations by Fast Computing Machines
• Spherical Hellinger--Kantorovich Gradient Flows
• The Wasserstein-Fisher-Rao Metric for Waveform Based Earthquake Location
• Optimal Transport