Related papers: Efficient Trajectory Inference in Wasserstein Spac…
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox…
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…
Particle tracing through numerical integration is a well-known approach to generating pathlines for visualization. However, for particle simulations, the computation of pathlines is expensive, since the interpolation method is complicated…
We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…
We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…
It can be shown that Stable Diffusion has a permutation-invariance property with respect to the rows of Contrastive Language-Image Pretraining (CLIP) embedding matrices. This inspired the novel observation that these embeddings can…
This paper investigates a time discrete variational model for splines in Wasserstein spaces to interpolate probability measures. Cubic splines in Euclidean space are known to minimize the integrated squared acceleration subject to a set of…
Ray tracing is increasingly utilized in wireless system simulations to estimate channel paths. In large-scale simulations with complex environments, ray tracing at high resolution can be computationally demanding. To reduce the computation,…
We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…
Sparsity is a common issue in many trajectory datasets, including human mobility data. This issue frequently brings more difficulty to relevant learning tasks, such as trajectory imputation and prediction. Nowadays, little existing work…
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…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
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…
Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial…
Trajectory inference investigates how to interpolate paths between observed timepoints of dynamical systems, such as temporally resolved population distributions, with the goal of inferring trajectories at unseen times and better…
This paper explores an efficient Lagrangian approach for evolving point cloud data on smooth manifolds. In this preliminary study, we focus on analyzing plane curves, and our ultimate goal is to provide an alternative to the conventional…
Patterns and nonlinear waves, such as spots, stripes, and rotating spirals, arise prominently in many natural processes and in reaction-diffusion models. Our goal is to compute boundaries between parameter regions with different prevailing…
We propose to study and promote the robustness of a model as per its performance through the interpolation of training data distributions. Specifically, (1) we augment the data by finding the worst-case Wasserstein barycenter on the…
We present a principled study on establishing a recursive Bayesian estimation scheme using B-splines in Euclidean spaces. The use of recurrent control points as the state vector is first conceptualized in a recursive setting. This enables…