Related papers: Bounding Optimality Gap in Stochastic Optimization…

In this paper we describe two bootstrap methods for massive data sets. Naive applications of common resampling methodology are often impractical for massive data sets due to computational burden and due to complex patterns of inhomogeneity.…

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…

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

Traditionally, stochastic approximation schemes for SVIs have relied on strong monotonicity and Lipschitzian properties of the underlying map. In contrast, we consider monotone stochastic variational inequality (SVI) problems where the…

We characterize the statistical bootstrap for the estimation of information-theoretic quantities from data, with particular reference to its use in the study of large-scale social phenomena. Our methods allow one to preserve, approximately,…

A large class of stochastic programs involve optimizing an expectation taken with respect to an underlying distribution that is unknown in practice. One popular approach to addressing the distributional uncertainty, known as the…

The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations with random inputs. After constructing a compact set that contains the SAA…

Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions…

The Stratified Bootstrap Test (SBT) provides a nonparametric, resampling-based framework for assessing the stability of group-specific ranking patterns in multivariate survey or rating data. By repeatedly resampling observations and…

Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…

We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses…

The planted coloring problem is a prototypical inference problem for which thresholds for Bayes optimal algorithms, like Belief Propagation (BP), can be computed analytically. In this paper, we analyze the limits and performances of the…

This paper is a study on solutions of the Sample Average Approximation Method to solve compound stochastic programs. We derive nonasymptotic upper estimates for probabilities of the approximation errors. The results depend on the sample…

The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. In addition to the standard…

Bayesian optimization (BO) is a popular, sample-efficient technique for expensive, black-box optimization. One such problem arising in manufacturing is that of maximizing the reliability, or equivalently minimizing the probability of a…

We consider the problem of finding confidence intervals for the risk of forecasting the future of a stationary, ergodic stochastic process, using a model estimated from the past of the process. We show that a bootstrap procedure provides…

Parametric empirical Bayes (EB) estimators have been widely used in variety of fields including small area estimation, disease mapping. Since EB estimator is constructed by plugging in the estimator of parameters in prior distributions, it…

Data-driven stochastic optimization is ubiquitous in machine learning and operational decision-making problems. Sample average approximation (SAA) and model-based approaches such as estimate-then-optimize (ETO) or integrated…

We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…