6 papers
Quantitative Stability of Many-Marginal Schrodinger Bridge
Rentian Yao, Young-Heon Kim, Geoffrey Schiebinger
In this paper, we explore quantitative stability of multi-marginal Schrödinger bridges with respect to the marginal constraints. We focus on the case where the number of marginal…
Statistical Analysis of the Sinkhorn Iterations for Two-Sample Schrödinger Bridge Estimation
Ibuki Maeda, Rentian Yao, Atsushi Nitanda
The Schrödinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorith…
Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs
Rentian Yao, Young--Heon Kim, Geoffrey Schiebinger
In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE)…
Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization
Kaheon Kim, Rentian Yao, Changbo Zhu +1
The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability…
Learning Density Evolution from Snapshot Data
Rentian Yao, Atsushi Nitanda, Xiaohui Chen +1
Motivated by learning dynamical structures from static snapshot data, this paper presents a distribution-on-scalar regression approach for estimating the density evolution of a sto…
Wasserstein Proximal Coordinate Gradient Algorithms
Rentian Yao, Xiaohui Chen, Yun Yang
Motivated by approximation Bayesian computation using mean-field variational approximation and the computation of equilibrium in multi-species systems with cross-interaction, this…