Related papers: Computing Capacity-Cost Functions for Continuous C…

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…

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…

Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation…

We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…

We study the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in computing the Wasserstein barycenter of $m$ discrete probability measures supported on a finite metric space of size $n$. We show first that the…

The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…

Penalizing complexity (PC) priors provide a principled framework for reducing model complexity by penalizing the Kullback--Leibler Divergence (KLD) between a ``simple'' base model and a more complex model. However, constructing priors by…

We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…

Designing experiments that systematically gather data from complex physical systems is central to accelerating scientific discovery. While Bayesian experimental design (BED) provides a principled, information-based framework that integrates…

Wasserstein barycentres represent average distributions between multiple probability measures for the Wasserstein distance. The numerical computation of Wasserstein barycentres is notoriously challenging. A common approach is to use…

We investigate here the optimal transportation problem on configuration space for the quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is finite, there exists one unique optimal measure and that this…

This paper recalls the proximal point method. We study two iterative algorithms: the Blahut-Arimoto algorithm for computing the capacity of arbitrary discrete memoryless channels, as an example of an iterative algorithm working with…

In our previous work, we presented a Blahut-Arimoto type algorithm for computing the discrete memoryless (DM) classical-quantum channel capacity. And the speed of convergence is analyzed. In this paper, we present numerical experiment to…

We develop novel neural network-based implicit particle methods to compute high-dimensional Wasserstein-type gradient flows with linear and nonlinear mobility functions. The main idea is to use the Lagrangian formulation in the…

Motivated by the 2D class averaging problem in single-particle cryo-electron microscopy (cryo-EM), we present a k-means algorithm based on a rotationally-invariant Wasserstein metric for images. Unlike existing methods that are based on…

One of the fundamental problems of information theory, since its foundation by Shannon in 1948, has been the computation of the capacity of a discrete memoryless channel, a quantity expressing the maximum rate at which information can…

The paper first recalls the Blahut Arimoto algorithm for computing the capacity of arbitrary discrete memoryless channels, as an example of an iterative algorithm working with probability density estimates. Then, a geometrical…

This paper studies the capacities of input-driven finite-state channels, i.e., channels whose current state is a time-invariant deterministic function of the previous state and the current input. We lower bound the capacity of such a…

A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…