arXiv subjects

Luis G. Crespo

Publications and source records attributed to Luis G. Crespo.

4 recordsLinked to original sources

arXiv2026

Quantification and Decomposition of Uncertainty Using Sliced-Normal Distribution: With Applications to NASA Data

Modeling multivariate distributions with nonlinear dependence, multimodality, and tractable analytical structure for downstream applications is a central challenge in uncertainty quantification. Sliced Normal (SN) distributions were introduced in prior works at the National Aeronautics and Space Administration (NASA) to address this need by representing densities through polynomial feature maps. This construction provides a compact algebraic alternative to more opaque generative models, while retaining the ability to capture nonlinear parameter dependencies and multi-modal behavior. In this paper, we build on the SN framework and develop several improvements that make the approach more reliable and scalable. First, we reformulate SN parameter estimation as a convex optimization problem over a positive semidefinite matrix, replacing the original nonconvex likelihood search with a formulation amenable to standard optimization tools. Second, we clarify the expressive power of the SN class by connecting polynomial log-density modeling to a Stone--Weierstrass-type universal approximation argument on compact domains. Third, we propose a high-dimensional fitting procedure that partitions variables into approximately independent groups, fits SN models within each subgroup, and then assembles the subgroup models through a cross-block completion step to recover residual dependence. We demonstrate the resulting SN modeling pipeline on NASA loss-of-control flight data, where the method captures nonlinear dependence patterns in both low-dimensional slices and a higher-dimensional block-assembled model.

stat.ME↗

arXiv2026

Robust Design in the Presence of Aleatoric and Epistemic Uncertainty

This paper proposes strategies for designing a system whose computational model is subject to aleatory and epistemic uncertainty. Aleatory variables, which are caused by randomness in physical parameters, are draws from a possibly unknown distribution; whereas epistemic variables, which are caused by ignorance in the value of fixed parameters, are free to take any value in a bounded set. Chance-constrained formulations enforcing the system requirements at a finite number of realizations of the uncertain parameters are proposed. These formulations trade off a lower objective value against a reduced robustness by eliminating an optimally chosen subset of such realizations. Risk-aware designs are obtained by accounting for the severity of the requirement violations resulting from this elimination process. Furthermore, we propose a computationally efficient design approach in which the training dataset is sequentially updated according to the results of high-fidelity reliability analyses of suboptimal designs. Robustness is evaluated by using Monte Carlo analysis and Robust Scenario Theory, with the latter approach accounting for the infinitely many values that the epistemic variables can take.

stat.ME↗

arXiv2025

A Data-driven Approach to Risk-aware Robust Design

This paper proposes risk-averse and risk-agnostic formulations to robust design in which solutions that satisfy the system requirements for a set of scenarios are pursued. These scenarios, which correspond to realizations of uncertain parameters or varying operating conditions, can be obtained either experimentally or synthetically. The proposed designs are made robust to variations in the training data by considering perturbed scenarios. This practice allows accounting for error and uncertainty in the measurements, thereby preventing data overfitting. Furthermore, we use relaxation to trade-off a lower optimal objective value against lesser robustness to uncertainty. This is attained by eliminating a given number of optimally chosen outliers from the dataset, and by allowing the perturbed scenarios to violate the requirements with an acceptably small probability. For instance, we can seek a design that satisfies the requirements for as many perturbed scenarios as possible, or pursue a riskier design that attains a lower objective value in exchange for a few scenarios violating the requirements. These ideas are illustrated by considering the design of an aeroelastic wing.

math.OC↗

arXiv2025

Risk Analysis and Design Against Adversarial Actions

Learning models capable of providing reliable predictions in the face of adversarial actions has become a central focus of the machine learning community in recent years. This challenge arises from observing that data encountered at deployment time often deviate from the conditions under which the model was trained. In this paper, we address deployment-time adversarial actions and propose a versatile, well-principled framework to evaluate the model's robustness against attacks of diverse types and intensities. While we initially focus on Support Vector Regression (SVR), the proposed approach extends naturally to the broad domain of learning via relaxed optimization techniques. Our results enable an assessment of the model vulnerability without requiring additional test data and operate in a distribution-free setup. These results not only provide a tool to enhance trust in the model's applicability but also aid in selecting among competing alternatives. Later in the paper, we show that our findings also offer useful insights for establishing new results within the out-of-distribution framework.

cs.LG↗