相关论文: Optimal Uncertainty Size in Distributionally Robus…

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…

Many important computer vision applications are naturally formulated as regression problems. Within medical imaging, accurate regression models have the potential to automate various tasks, helping to lower costs and improve patient…

Whilst an abundance of techniques have recently been proposed to generate counterfactual explanations for the predictions of opaque black-box systems, markedly less attention has been paid to exploring the uncertainty of these generated…

Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an…

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer…

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

Recent advances in the fields of robotics and automation have spurred significant interest in robust state estimation. To enable robust state estimation, several methodologies have been proposed. One such technique, which has shown…

This paper expands the notion of robust profit opportunities in financial markets to incorporate distributional uncertainty using Wasserstein distance as the ambiguity measure. Financial markets with risky and risk-free assets are…

Learning probability distributions on the weights of neural networks (NNs) has recently proven beneficial in many applications. Bayesian methods, such as Stein variational gradient descent (SVGD), offer an elegant framework to reason about…

We study the {\em robust proper learning} of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis…

There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…

We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty…

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…

We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…

We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density…

The problem of estimating certain distributions over $\{0,1\}^d$ is considered here. The distribution represents a quantum system of $d$ qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is…

Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…