Rentian Yao
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View article: Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs
Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs Open
In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE) with a constant diffusion coefficient, and with time depend…
View article: Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization
Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization Open
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 distributions. Computation of the unregularized barycenter …
View article: Convergence rate of the solution of multi-marginal Schrödinger bridge problem with marginal constraints from SDEs
Convergence rate of the solution of multi-marginal Schrödinger bridge problem with marginal constraints from SDEs Open
View article: Minimizing Convex Functionals over Space of Probability Measures via KL Divergence Gradient Flow
Minimizing Convex Functionals over Space of Probability Measures via KL Divergence Gradient Flow Open
Motivated by the computation of the non-parametric maximum likelihood estimator (NPMLE) and the Bayesian posterior in statistics, this paper explores the problem of convex optimization over the space of all probability distributions. We in…
View article: Mean-field Variational Inference via Wasserstein Gradient Flow
Mean-field Variational Inference via Wasserstein Gradient Flow Open
Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…
View article: Mean-Field Nonparametric Estimation of Interacting Particle Systems
Mean-Field Nonparametric Estimation of Interacting Particle Systems Open
This paper concerns the nonparametric estimation problem of the distribution-state dependent drift vector field in an interacting $N$-particle system. Observing single-trajectory data for each particle, we derive the mean-field rate of con…
View article: A Specific Duration and High-energy Sine Wave Model to Reflect the Awaking and Falling Asleep Moments of Human
A Specific Duration and High-energy Sine Wave Model to Reflect the Awaking and Falling Asleep Moments of Human Open
The process of falling asleep is complicated. Is there a mutation between sleep state and waking state? This paper applied a new specific duration and high-energy sine wave (SDHE) model based on single-channel brainwave to study this probl…