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Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique…

This paper explores optimal methods for obtaining one-dimensional (1D) powder pattern intensities from two-dimensional (2D) planar detectors with good estimates of their standard deviations. We describe methods to estimate uncertainties…

This paper proposes a new approach to address the problem of unmeasured confounding in spatial designs. Spatial confounding occurs when some confounding variables are unobserved and not included in the model, leading to distorted…

Uncertainty quantification, by means of confidence interval (CI) construction, has been a fundamental problem in statistics and also important in risk-aware decision-making. In this paper, we revisit the basic problem of CI construction,…

Among the many ways of quantifying uncertainty in a regression setting, specifying the full quantile function is attractive, as quantiles are amenable to interpretation and evaluation. A model that predicts the true conditional quantiles…

Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Since radio interferometric imaging requires…

We propose an unfolded accelerated projected-gradient descent procedure to estimate model and algorithmic parameters for image super-resolution and molecule localization problems in image microscopy. The variational lower-level constraint…

Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…

For an AI system to be reliable, the confidence it expresses in its decisions must match its accuracy. To assess the degree of match, examples are typically binned by confidence and the per-bin mean confidence and accuracy are compared.…

Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…

Obtaining accurate estimates of machine learning model uncertainties on newly predicted data is essential for understanding the accuracy of the model and whether its predictions can be trusted. A common approach to such uncertainty…

Mammographic screening is an effective method for detecting breast cancer, facilitating early diagnosis. However, the current need to manually inspect images places a heavy burden on healthcare systems, spurring a desire for automated…

Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Statistical sampling approaches to perform…

There is a well-known series expansion (Neumann series) in functional analysis for perturbative inversion of specific operators on Banach spaces. However, operators that appear in signal processing (e.g. folding and convolution of…

Uncertainty in medical image segmentation is inherently non-uniform, with boundary regions exhibiting substantially higher ambiguity than interior areas. Conventional training treats all pixels equally, leading to unstable optimization…

Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace…

Conformal Prediction (CP) is a distribution-free method for constructing prediction sets with marginal finite-sample coverage guarantees, making it a suitable framework for reliable uncertainty quantification in safety-critical object…

"The Price of Robustness" by Bertsimas and Sim represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each…

Robust Optimal Control (ROC) with adjustable uncertainties has proven to be effective in addressing critical challenges within modern energy networks, especially the reserve and provision problem. However, prior research on ROC with…

Solving differential equations from limited or noisy data remains a key challenge for physics-informed neural networks (PINNs), which are typically applied to already known and smooth solutions. In this work, we explore Bayesian PINNs and…