Related papers: Accelerated Regularized Wasserstein Proximal Sampl…
We consider the problem of sampling from a density of the form $p(x) \propto \exp(-f(x)- g(x))$, where $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a smooth and strongly convex function and $g: \mathbb{R}^d \rightarrow \mathbb{R}$ is a…
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…
A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
Comparing two probability measures supported on heterogeneous spaces is an increasingly important problem in machine learning. Such problems arise when comparing for instance two populations of biological cells, each described with its own…
We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…
Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-asymptotic analysis in the $L^2$ Wasserstein distance of…
Communication is one of the bottlenecks of distributed optimisation and learning. To overcome this bottleneck, we propose a novel quantization method that transforms a vector into a sample of components' indices drawn from a categorical…
Wasserstein distance-based distributionally robust optimization (DRO) has received much attention lately due to its ability to provide a robustness interpretation of various learning models. Moreover, many of the DRO problems that arise in…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
We present an optimization algorithm that can identify a global minimum of a potentially nonconvex smooth function with high probability, assuming the Gibbs measure of the potential satisfies a logarithmic Sobolev inequality. Our…
In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our…
In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging…
We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…
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…
The Gromov-Wasserstein (GW) framework adapts ideas from optimal transport to allow for the comparison of probability distributions defined on different metric spaces. Scalable computation of GW distances and associated matchings on graphs…
We present alphaPDE, a new multivariate analysis technique for parameter estimation. The method is based on a direct construction of joint probability densities of known variables and the parameters to be estimated. We show how posterior…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
An Automated Sliced Gibbs framework is proposed for fully automated Markov chain Monte Carlo sampling from arbitrary finite dimensional probability kernels. The method targets unnormalized, non-smooth, heavy tailed, and highly multimodal…