Related papers: The data-driven Schroedinger bridge
Conditional generative models represent a significant advancement in the field of machine learning, allowing for the controlled synthesis of data by incorporating additional information into the generation process. In this work we introduce…
Machine learning-based unfolding has enabled unbinned and high-dimensional differential cross section measurements. Two main approaches have emerged in this research area: one based on discriminative models and one based on generative…
We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint…
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT problem, the entropic OT problem, which allows to implement…
Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized…
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 dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…
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…
The theory of Schroedinger bridges for diffusion processes is extended to classical and quantum discrete-time Markovian evolutions. The solution of the path space maximum entropy problems is obtained from the a priori model in both cases…
We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…
Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…
Learning generative models in settings where the source and target distributions are only specified through unpaired samples is gaining in importance. Here, one frequently-used model are Schr\"odinger bridges (SB), which represent the most…
The Schr\"{o}dinger Bridge Problem (SBP), which can be understood as an entropy-regularized optimal transport, seeks to compute stochastic dynamic mappings connecting two given distributions. SBP has shown significant theoretical importance…
Flow matching and diffusion bridge models have emerged as leading paradigms in generative speech enhancement, modeling stochastic processes between paired noisy and clean speech signals based on principles such as flow matching, score…
We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an…
We propose and study a system of Schr\"odinger's problems and functional equations in probability theory. More precisely, we consider a system of variational problems of relative entropies for probability measures on a Euclidean space with…
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…
Modern methods of generative modelling and unpaired data translation based on Schr\"odinger bridges and stochastic optimal control theory aim to transform an initial density to a target one in an optimal way. In the present paper, we assume…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…