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Reliability-based design optimization (RBDO) is traditionally formulated as a nested optimization and reliability problem. Although surrogate models are generally employed to improve efficiency, the approach remains computationally…
We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…
The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…
A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead,…
This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…
We consider the problem of estimating the trace of a matrix function $f(A)$. In certain situations, in particular if $f(A)$ cannot be well approximated by a low-rank matrix, combining probing methods based on graph colorings with stochastic…
External pilot trials of complex interventions are used to help determine if and how a confirmatory trial should be undertaken, providing estimates of parameters such as recruitment, retention and adherence rates. The decision to progress…
We show that the exact worst-case performance of fixed-step first-order methods for unconstrained optimization of smooth (possibly strongly) convex functions can be obtained by solving convex programs. Finding the worst-case performance of…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
In decommissioning projects of nuclear facilities, the radiological characterisation step aims to estimate the quantity and spatial distribution of different radionuclides. To carry out the estimation, measurements are performed on site to…
A number of problems in quantum state and system identification are addressed. Specifically, it is shown that the maximum likelihood estimation (MLE) approach, already known to apply to quantum state tomography, is also applicable to…
In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
We study momentum-based first-order optimization algorithms in which the iterations utilize information from the two previous steps and are subject to an additive white noise. This setup uses noise to account for uncertainty in either…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an $\epsilon$-$expectedly\ feasible\ stochastic\ optimal$ solution, in which…
We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…