相关论文: Inverse Problems Over Probability Measure Space

We consider the rate-distortion function for lossy source compression, as well as the channel capacity for error correction, through the lens of distributional robustness. We assume that the distribution of the source or of the additive…

We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images,…

For linear inverse problems with Gaussian priors and Gaussian observation noise, the posterior is Gaussian, with mean and covariance determined by the conditioning formula. Using the Feldman-Hajek theorem, we analyse the prior-to-posterior…

We study an inverse problem that consists in estimating the first (zero-order) moment of some R2-valued distribution m supported within a closed interval S $\subset$ R, from partial knowledge of the solution to the Poisson-Laplace partial…

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…

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…

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…

In prescriptive analytics, the decision-maker observes historical samples of $(X, Y)$, where $Y$ is the uncertain problem parameter and $X$ is the concurrent covariate, without knowing the joint distribution. Given an additional covariate…

Despite superior performance in many situations, deep neural networks are often vulnerable to adversarial examples and distribution shifts, limiting model generalization ability in real-world applications. To alleviate these problems,…

Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…

In the classical source coding problem, the compressed source is reconstructed at the decoder with respect to some distortion metric. Motivated by settings in which we are interested in more than simply reconstructing the compressed source,…

The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…

We study the inverse optimal control problem in social sciences: we aim at learning a user's true cost function from the observed temporal behavior. In contrast to traditional phenomenological works that aim to learn a generative model to…

The inverse problem of determining the unknown potential $f>0$ in the partial differential equation $$\frac{\Delta}{2} u - fu =0 \text{ on } \mathcal O ~~\text{s.t. } u = g \text { on } \partial \mathcal O,$$ where $\mathcal O$ is a bounded…

Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein…

Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…

We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial…

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…