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Although Potent purports to use only radial velocities in reconstructing the potential velocity field of galaxies, the derivation of transverse components is implicit in the smoothing procedures adopted. Thus the possibility arises of using…

We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…

Parameter estimation is a fundamental challenge in machine learning, crucial for tasks such as neural network weight fitting and Bayesian inference. This paper focuses on the complexity of estimating translation $\boldsymbol{\mu} \in…

This paper presents a novel distribution-agnostic Wasserstein distance-based estimation framework. The goal is to determine an optimal map combining prior estimate with measurement likelihood such that posterior estimation error optimally…

The performance of machine learning (ML) models critically depends on the quality and representativeness of the training data. In applications with multiple heterogeneous data generating sources, standard ML methods often learn spurious…

Minimizing functionals in the space of probability distributions can be done with Wasserstein gradient flows. To solve them numerically, a possible approach is to rely on the Jordan-Kinderlehrer-Otto (JKO) scheme which is analogous to the…

This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou-Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport.…

Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive…

Determinantal point processes (DPPs) have received significant attention as an elegant probabilistic model for discrete subset selection. Most prior work on DPP learning focuses on maximum likelihood estimation (MLE). While efficient and…

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

The $E$-optimality criterion for a regression model maximizes the smallest eigenvalue of the information matrix and becomes non-differentiable when this eigenvalue has multiplicity greater than one. Working in the $2$-Wasserstein space, we…

The purpose of this paper is to answer a few open questions in the interface of kernel methods and PDE gradient flows. Motivated by recent advances in machine learning, particularly in generative modeling and sampling, we present a rigorous…

In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…

Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian…

Wasserstein gradient flows on probability measures have found a host of applications in various optimization problems. They typically arise as the continuum limit of exchangeable particle systems evolving by some mean-field interaction…

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…

Graph generation has emerged as a critical task in fields ranging from drug discovery to circuit design. Contemporary approaches, notably diffusion and flow-based models, have achieved solid graph generative performance through constructing…

We formulate a class of velocity-free finite-particle methods for mass transport problems based on a time-discrete incremental variational principle that combines entropy and the cost of particle transport, as measured by the Wasserstein…

A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that…