Related papers: Wasserstein-based Projections with Applications to…
In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise.…
Gaussian process (GP) regression is widely used for uncertainty quantification, yet the standard formulation assumes noise-free covariates. When inputs are measured with error, this errors-in-variables (EIV) setting can lead to…
Wasserstein Policy Optimization (WPO) is a recently proposed reinforcement learning algorithm that leverages Wasserstein gradient flows to optimize stochastic policies in continuous action spaces. Despite its empirical success, the…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
Plug-and-play (PnP) is a non-convex framework that combines ADMM or other proximal algorithms with advanced denoiser priors. Recently, PnP has achieved great empirical success, especially with the integration of deep learning-based…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…
We show the convergence of Wasserstein inverse reinforcement learning for multi-objective optimizations with the projective subgradient method by formulating an inverse problem of the multi-objective optimization problem. In addition, we…
There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…
We study policy gradient methods for continuous-action, entropy-regularized reinforcement learning through the lens of Wasserstein geometry. Starting from a Wasserstein proximal update, we derive Wasserstein Proximal Policy Gradient (WPPG)…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
We propose a novel multi-layer neural network architecture that gives a promising neural network empowered optimization approach to the image restoration problem. The proposed architecture is motivated by the recent study of monotone…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
In this paper, we present a novel variational plug-and-play algorithm for Poisson inverse problems. Our approach minimizes an explicit functional which is the sum of a Kullback-Leibler data fidelity term and a regularization term based on a…
In this work we propose an efficient stochastic plug-and-play (PnP) algorithm for imaging inverse problems. The PnP stochastic gradient descent methods have been recently proposed and shown improved performance in some imaging applications…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
Plug-and-Play (PnP) is a non-convex optimization framework that combines proximal algorithms, for example, the alternating direction method of multipliers (ADMM), with advanced denoising priors. Over the past few years, great empirical…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
It's well-known that inverse problems are ill-posed and to solve them meaningfully, one has to employ regularization methods. Traditionally, popular regularization methods are the penalized Variational approaches. In recent years, the…
Computing Wasserstein barycenters of discrete measures has recently attracted considerable attention due to its wide variety of applications in data science. In general, this problem is NP-hard, calling for practical approximative…