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High-dimensional interpolation problems appear in various applications of uncertainty quantification, stochastic optimization and machine learning. Such problems are computationally expensive and request the use of adaptive grid generation…

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set,…

This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic…

The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…

Using Machine Learning systems in the real world can often be problematic, with inexplicable black-box models, the assumed certainty of imperfect measurements, or providing a single classification instead of a probability distribution. This…

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…

Sparsity is a desirable attribute. It can lead to more efficient and more effective representations compared to the dense model. Meanwhile, learning sparse latent representations has been a challenging problem in the field of computer…

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis…

We develop a simple and unified framework for nonlinear variable selection that incorporates uncertainty in the prediction function and is compatible with a wide range of machine learning models (e.g., tree ensembles, kernel methods, neural…

As a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also…

We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…

In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…

The use of deep learning for medical imaging has seen tremendous growth in the research community. One reason for the slow uptake of these systems in the clinical setting is that they are complex, opaque and tend to fail silently. Outside…

Robust optimization is a method for optimization under uncertainties in engineering systems and designs for applications ranging from aeronautics to nuclear. In a robust design process, parameter variability (or uncertainty) is incorporated…

Gamma uncertainty sets have been introduced for adjusting the degree of conservatism of robust counterparts of (discrete) linear programs. The contribution of this paper is a generalization of this approach to (mixed integer) nonlinear…

We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…

Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…

Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…