Related papers: Gradient Flows for Frame Potentials on the Wassers…
Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
Many machine learning problems can be seen as approximating a \textit{target} distribution using a \textit{particle} distribution by minimizing their statistical discrepancy. Wasserstein Gradient Flow can move particles along a path that…
On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natural extension of cubic splines to the Wasserstein space, we…
A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this…
Robots often rely on a repertoire of previously-learned motion policies for performing tasks of diverse complexities. When facing unseen task conditions or when new task requirements arise, robots must adapt their motion policies…
Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional methods relying on full Wasserstein gradients often suffer from…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
This thesis analyze the Wasserstein gradient flow of a functional defined as a double convolution of a non-smooth repulsive interaction potential. To be more precise, the potential under investigation has a -|x| behavior close to the…
We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe the solution depending on the choice of the ground metric…
This paper presents a groundbreaking approach to causal inference by integrating continuous normalizing flows (CNFs) with parametric submodels, enhancing their geometric sensitivity and improving upon traditional Targeted Maximum Likelihood…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
We propose a new notion of the formal tangent space to the Wasserstein space $\mathcal{P}(X)$ at a given measure. Modulo an integrability condition, we say that this tangent space is made of functions over $X$ which are valued in the…
A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of the square Wasserstein metric. In this paper, we develop a class of transport metrics that have better convexity properties and use these metrics to…
Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…
We study the Wasserstein gradient flow of semi-discrete energies in the space of probability measures, that is functionals depending on two measures-one being an absolutely continuous density and the other an atomic measure. These energies…
We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…