Related papers: Second-Order Uncertainty Quantification: A Distanc…
In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
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…
Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
Optimal transport theory has recently been extended to quantum settings, where the density matrices generalize the probability measures. In this paper, we study the computational aspects of the order 2 quantum Wasserstein distance,…
In this study, we consider an optimization problem with uncertainty dependent on decision variables, which has recently attracted attention due to its importance in machine learning and pricing applications. In this problem, the gradient of…
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…
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…
This book chapter introduces the principles and practical applications of uncertainty quantification in machine learning. It explains how to identify and distinguish between different types of uncertainty and presents methods for…
Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to a specific operating point,…
In this article, we study the approximation of a probability measure $\mu$ on $\mathbb{R}^{d}$ by its empirical measure $\hat{\mu}_{N}$ interpreted as a random quantization. As error criterion we consider an averaged $p$-th moment…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
We investigate the in-distribution generalization of machine learning algorithms. We depart from traditional complexity-based approaches by analyzing information-theoretic bounds that quantify the dependence between a learning algorithm and…
Despite AI's impressive achievements, including recent advances in generative and large language models, there remains a significant gap in the ability of AI systems to handle uncertainty and generalize beyond their training data. AI models…
This paper discusses a new measure that is adaptable to certain intervalic probability frameworks, possibility theory, and belief theory. As such, it has the potential for wide use in knowledge engineering, expert systems, and related…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…