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The importance of accurately quantifying forecast uncertainty has motivated much recent research on probabilistic forecasting. In particular, a variety of deep learning approaches has been proposed, with forecast distributions obtained as…

We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…

Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…

We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive…

This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to…

This paper introduces a novel, computationally-efficient algorithm for predictive inference (PI) that requires no distributional assumptions on the data and can be computed faster than existing bootstrap-type methods for neural networks.…

This paper investigates the accuracy of bootstrap-based bias correction of persistence measures for long memory fractionally integrated processes. The bootstrap method is based on the semi-parametric sieve approach, with the dynamics in the…

We study a class of backtests for forecast distributions in which the test statistic depends on a spectral transformation that weights exceedance events by a function of the modeled probability level. The weighting scheme is specified by a…

We study U.S. Treasury yield curve forecasting under distributional uncertainty and recast forecasting as an operations research and managerial decision problem. Rather than minimizing average forecast error, the forecaster selects a…

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…

Selective prediction, where a model has the option to abstain from making a decision, is crucial for machine learning applications in which mistakes are costly. In this work, we focus on distributional regression and introduce a framework…

Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the…

The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…

Neural networks predictions are unreliable when the input sample is out of the training distribution or corrupted by noise. Being able to detect such failures automatically is fundamental to integrate deep learning algorithms into robotics.…

Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples…

In stochastic optimal control (SOC), uncertainty may arise from incomplete knowledge of the true probability distribution of the underlying environment, which is known as Knightian or epistemic uncertainty. Distributionally robust optimal…

Conformal prediction provides a framework for uncertainty quantification, specifically in the forms of prediction intervals and sets with distribution-free guaranteed coverage. While recent cross-conformal techniques such as CV+ and…

In many fairness and distribution robustness problems, one has access to labeled data from multiple source distributions yet the test data may come from an arbitrary member or a mixture of them. We study the problem of constructing a…

This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in…

Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…