相关论文: Convergence Rate of the Solution of Multi-marginal…
Schr\"{o}dinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We…
We characterize the Schr\"odinger bridge problems by a family of Mckean-Vlasov stochastic control problems with no terminal time distribution constraint. In doing so, we use the theory of Hilbert space embeddings of probability measures and…
In this work, we revisit the discrete-time Schr\"{o}dinger Bridge (SB) and Density Steering (DS) problems for Gaussian mixture model (GMM) boundary distributions. Building on the existing literature, we construct a set of feasible Markovian…
We consider the problem to identify the most likely flow in phase space, of (inertial) particles under stochastic forcing, that is in agreement with spatial (marginal) distributions that are specified at a set of points in time. The…
Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual…
It is a crucial challenge to reconstruct population dynamics using unlabeled samples from distributions at coarse time intervals. Recent approaches such as flow-based models or Schr\"odinger Bridge (SB) models have demonstrated appealing…
In this paper, we explore quantitative stability of multi-marginal Schr\"odinger bridges with respect to the marginal constraints. We focus on the case where the number of marginal constraints is large (i.e. ``many-marginals"). When this…
The Mean-Field Schrodinger Bridge (MFSB) problem is an optimization problem aiming to find the minimum effort control policy to drive a McKean-Vlassov stochastic differential equation from one probability measure to another. In the context…
Schr\"{o}dinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular method to numerically solve the Schr\"{o}dinger bridge…
Stochastic flows of an advective-diffusive nature are ubiquitous in physical sciences. Of particular interest is the problem to reconcile observed marginal distributions with a given prior posed by E. Schrodinger in 1932/32 and known as the…
The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent…
The classical Schrodinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and…
Schr\"odinger bridges (SBs) provide an elegant framework for modeling the temporal evolution of populations in physical, chemical, or biological systems. Such natural processes are commonly subject to changes in population size over time…
The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates…
Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher…
The Schr\"odinger bridge problem (SBP) seeks to find the measure $\hat{\mathbf{P}}$ on a certain path space which interpolates between state-space distributions $\rho_0$ at time $0$ and $\rho_T$ at time $T$ while minimizing the KL…
Motivated by modern machine learning applications where we only have access to empirical measures constructed from finite samples, we relax the marginal constraints of the classical Schr\"odinger bridge problem by penalizing the transport…
The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…
Diffusion Schr\"odinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms…
In this paper, we study averaging principles for a class of time-inhomogeneous stochastic differential equations (SDEs) with slow and fast time-scales, where the drift term in the fast component is time-dependent and only partially…