Importance Sampling and its Optimality for Stochastic Simulation Models

We consider the problem of estimating an expected outcome from a stochastic simulation model. Our goal is to develop a theoretical framework on importance sampling for such estimation. By investigating the variance of an importance sampling estimator, we propose a two-stage procedure that involves a regression stage and a sampling stage to construct the final estimator. We introduce a parametric and a nonparametric regression estimator in the first stage and study how the allocation between the two stages affects the performance of the final estimator. We analyze the variance reduction rates and derive oracle properties of both methods. We evaluate the empirical performances of the methods using two numerical examples and a case study on wind turbine reliability evaluation.Comment: 37 pages, 6 figures, 2 tables. Accepted to the Electronic Journal of Statistic

A nonparametric Bayesian approach toward robot learning by demonstration

In the past years, many authors have considered application of machine learning methodologies to effect robot learning by demonstration. Gaussian mixture regression (GMR) is one of the most successful methodologies used for this purpose. A major limitation of GMR models concerns automatic selection of the proper number of model states, i.e., the number of model component densities. Existing methods, including likelihood- or entropy-based criteria, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori. Under this motivation, to resolve the aforementioned issues of GMR-based methods for robot learning by demonstration, in this paper we introduce a nonparametric Bayesian formulation for the GMR model, the Dirichlet process GMR model. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally investigate its efficacy as a robot learning by demonstration methodology, considering a number of demanding robot learning by demonstration scenarios

Penalized Likelihood and Bayesian Function Selection in Regression Models

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive predictors has been considered only more recently. Several competing suggestions have been developed at about the same time and often do not refer to each other. This article provides a state-of-the-art review on function selection, focusing on penalized likelihood and Bayesian concepts, relating various approaches to each other in a unified framework. In an empirical comparison, also including boosting, we evaluate several methods through applications to simulated and real data, thereby providing some guidance on their performance in practice