Related papers: Uses of Sub-sample Estimates to Reduce Errors in S…
Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
An asymptotically optimal sampling-based planner employs sampling to solve robot motion planning problems and returns paths with a cost that converges to the optimal solution cost, as the number of samples approaches infinity. This…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realise the position suggested by the optimal portfolios, he/she needs to estimate the unknown…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds…
We study statistical properties of the optimal value of the Sample Average Approximation. The focus is on the tail function of the absolute error induced by the Sample Average Approximation, deriving upper estimates of its outcomes…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower…
Almost every software system provides configuration options to tailor the system to the target platform and application scenario. Often, this configurability renders the analysis of every individual system configuration infeasible. To…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…