相关论文: Statistical Mechanics of the Sub-Optimal Transport
Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…
Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…
An algorithmic limit of compressed sensing or related variable-selection problems is analytically evaluated when a design matrix is given by an overcomplete random matrix. The replica method from statistical mechanics is employed to derive…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…
Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…
In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…
We propose a general framework of mass transport between vector-valued measures, which will be called simultaneous optimal transport (SOT). The new framework is motivated by the need to transport resources of different types simultaneously,…
Optimal Transport (OT) is a resource allocation problem with applications in biology, data science, economics and statistics, among others. In some of the applications, practitioners have access to samples which approximate the continuous…
The Self-Optimal-Transport (SOT) feature transform is designed to upgrade the set of features of a data instance to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order…
Understanding how cities transition from free-flowing to congested traffic remains a central open problem in urban science. Here we show that city-scale congestion undergoes a reproducible nonlinear transition analogous to an order-disorder…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…