Related papers: Kriging measure-valued data with sparse observatio…
We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are non-intrusive, goal-oriented uncertainty quantification tools that…
We study the Wasserstein gradient flow of semi-discrete energies in the space of probability measures, that is functionals depending on two measures-one being an absolutely continuous density and the other an atomic measure. These energies…
Multi-fidelity Kriging model is a promising technique in surrogate-based design as it can balance the model accuracy and cost of sample preparation by fusing low- and high-fidelity data. However, the cost for building a multi-fidelity…
Robotic manipulation in dynamic and unstructured environments requires safety mechanisms that exploit what is known and what is uncertain about the world. Existing safety filters often assume full observability, limiting their applicability…
Assume that a Gaussian process $\xi$ is predicted from $n$ pointwise observations by intrinsic Kriging and that the volume of the excursion set of $\xi$ above a given threshold $u$ is approximated by the volume of the predictor. The first…
Converting an n-dimensional vector to a probability distribution over n objects is a commonly used component in many machine learning tasks like multiclass classification, multilabel classification, attention mechanisms etc. For this,…
We examine the infinite-dimensional optimization problem of finding a decomposition of a probability measure into K probability sub-measures to minimize specific loss functions inspired by applications in clustering and user grouping. We…
Wasserstein distance is a key metric for quantifying data divergence from a distributional perspective. However, its application in privacy-sensitive environments, where direct sharing of raw data is prohibited, presents significant…
Von Renesse and the author (Ann. Prob. '09) developed a second order calculus on the Wasserstein space P([0,1]) of probability measures on the unit interval. The basic objects of interest had been Dirichlet form, semigroup and continuous…
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…
Stochastic kriging has been widely employed for simulation metamodeling to predict the response surface of complex simulation models. However, its use is limited to cases where the design space is low-dimensional because, in general, the…
Statistical interpolation of chemical concentrations at new locations is an important step in assessing a worker's exposure level. When measurements are available from coastlines, as is the case in coastal clean-up operations in oil spills,…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
The success of autoregressive models largely depends on the effectiveness of vector quantization, a technique that discretizes continuous features by mapping them to the nearest code vectors within a learnable codebook. Two critical issues…
This work investigates the prediction performance of the kriging predictors. We derive some error bounds for the prediction error in terms of non-asymptotic probability under the uniform metric and $L_p$ metrics when the spectral densities…
Computing an ensemble of random fields using conditional simulation is an ideal method for retrieving accurate estimates of a field conditioned on available data and for quantifying the uncertainty of these realizations. Methods for…
In this paper we introduce some recent progresses on the convergence rate in Wasserstein distance for empirical measures of Markov processes. For diffusion processes on compact manifolds possibly with reflecting or killing boundary…