Related papers: Trajectory Inference with Smooth Schr\"odinger Bri…
We follow a research thread studying the predecessor problem on "smooth" distribution families. We propose a conceptually simpler solution utilizing well-known results from much better studied variant of the problem that assumes nothing…
We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data, which provide high…
Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…
Generalized Schr\"odinger Bridges (GSBs) are a fundamental mathematical framework used to analyze the most likely particle evolution based on the principle of least action including kinetic and potential energy. In parallel to their…
Metasurface inverse design is challenged by the intricate relationship between structural parameters and electromagnetic responses, as well as the high dimensionality of the optimization space. Local models, while commonly employed, quickly…
Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on…
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…
The Schr\"odinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport…
Leveraging connections between diffusion-based sampling, optimal transport, and stochastic optimal control through their shared links to the Schr\"odinger bridge problem, we propose novel objective functions that can be used to transport…
Quantum counterparts of Schrodinger's classical bridge problem have been around for the better part of half a century. During that time, several quantum approaches to this multifaceted classical problem have been introduced. In the present…
We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…
Learning dynamical systems from sparse observations is critical in numerous fields, including biology, finance, and physics. Even if tackling such problems is standard in general information fusion, it remains challenging for contemporary…
Entropy-regularized optimal transport, which has strong links to the Schr\"odinger bridge problem in statistical mechanics, enjoys a variety of applications from trajectory inference to generative modeling. A major driver of renewed…
We propose a novel generative model for time series based on Schr{\"o}dinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure…
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
Motivated by recent experimental developments in functional genomics, we construct and test a numerical technique for inferring it process pathways, in which one process calls another process, from time series data. We validate using a case…
This work studies the Schr\"odinger bridge problem for the kinematic equation on a compact connected Lie group. The objective is to steer a controlled diffusion between given initial and terminal densities supported over the Lie group while…
In this paper we establish relationships between four important concepts: (a) hitting time problems of Brownian motion, (b) 3-dimensional Bessel bridges, (c) Schr\"odinger's equation with linear potential, and (d) heat equation problems…