Related papers: Estimating a probability of failure with the conve…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In…
We consider the problem of estimating a parameter associated to a Bayesian inverse problem. Treating the unknown initial condition as a nuisance parameter, typically one must resort to a numerical approximation of gradient of the…
In various industrial contexts, estimating the distribution of unobserved random vectors Xi from some noisy indirect observations H(Xi) + Ui is required. If the relation between Xi and the quantity H(Xi), measured with the error Ui, is…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
We consider a trader who wants to direct his portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a black-box algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and…
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…
The learning curve expresses the error rate of a predictive modeling procedure as a function of the sample size of the training dataset. It typically is a decreasing, convex function with a positive limiting value. An estimate of the…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
In this study, a stochastic constitutive modeling approach for elastomeric materials is developed to consider uncertainty in material behavior and its prediction. This effort leads to a demonstration of the deterministic approaches error…
Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box''. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible…
Evaluating failure probability for complex engineering systems is a computationally intensive task. While the Monte Carlo method is easy to implement, it converges slowly and, hence, requires numerous repeated simulations of a complex…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
Bayesian optimization is a popular framework for efficiently tackling black-box search problems. As a rule, these algorithms operate by iteratively choosing what to evaluate next until some predefined budget has been exhausted. We…
We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto optimal solutions among a finite set of candidates for which the two objective outcomes have been observed with uncertainty (e.g.,…
The potential for cascading failure in power systems adds substantially to overall reliability risk. Monte Carlo sampling can be used with a power system model to estimate this impact, but doing so is computationally expensive. This paper…
Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and adversarial machine learning. While…
This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…