Related papers: Optimal transport for Gaussian mixture models
Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
Gaussian mixtures are widely used for approximating density functions in various applications such as density estimation, belief propagation, and Bayesian filtering. These applications often utilize Gaussian mixtures as initial…
This paper presents the first application of Gaussian Mixture Copula Models to the statistical modeling of driving scenarios for the safety validation of automated driving systems. Knowledge of the joint probability distribution of scenario…
Optimal transport has been one of the most exciting subjects in mathematics, starting from the 18th century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a…
We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…
We present a review of nonequilibrium phase transitions in mass-transport models with kinetic processes like fragmentation, diffusion, aggregation, etc. These models have been used extensively to study a wide range of physical problems. We…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
We investigate the 1D version of the notable Bressan's mixing conjecture, and introduce various formulation in the classical optimal transport setting, the branched optimal transport setting and a combinatorial optimization. In the discrete…
We explore the geometry of the Bures-Wasserstein space for potentially degenerate Gaussian measures on a separable Hilbert space. In this general setting, the optimal transport map is formally the subgradient of a convex function that is…
We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…
Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…
We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…
Recently, enthusiastic studies have devoted to texture synthesis using deep neural networks, because these networks excel at handling complex patterns in images. In these models, second-order statistics, such as Gram matrix, are used to…
This paper uses Gaussian mixture model instead of linear Gaussian model to fit the distribution of every node in Bayesian network. We will explain why and how we use Gaussian mixture models in Bayesian network. Meanwhile we propose a new…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…