Related papers: Sparsity for dynamic inverse problems on Wasserste…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein ($W_2$) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the…
Kullback-Leibler divergence (KL) regularization is widely used in reinforcement learning, but it becomes infinite under support mismatch and can degenerate in low-noise limits. Utilizing a unified information-geometric framework, we…
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…
We study a variety of Wasserstein distributionally robust optimization (WDRO) problems where the distributions in the ambiguity set are chosen by constraining their Wasserstein discrepancies to the empirical distribution. Using the notion…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
Experimental design is central to science and engineering. A ubiquitous challenge is how to maximize the value of information obtained from expensive or constrained experimental settings. Bayesian optimal experimental design (OED) provides…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
We consider probabilistic models for sequential observations which exhibit gradual transitions among a finite number of states. We are particularly motivated by applications such as human activity analysis where observed accelerometer time…
We study the reknown deconvolution problem of recovering a distribution function from independent replicates (signal) additively contaminated with random errors (noise), whose distribution is known. We investigate whether a Bayesian…
This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes…
In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…
Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…
We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…
We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…
We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and…