<div><b>1. A Closed-Loop Machine Learning and Compensation Framework for Geometric Accuracy Control of 3D Printed Products</b></div><div><b><br></b></div>Additive manufacturing (AM) systems enable direct printing of three-dimensional (3D) physical products from computer-aided design (CAD) models. Despite the many advantages that AM systems have over traditional manufacturing, one of their significant limitations that impedes their wide adoption is geometric inaccuracies, or shape deviations between the printed product and the nominal CAD model. Machine learning for shape deviations can enable geometric accuracy control of 3D printed products via the generation of compensation plans, which are modifications of CAD models informed by the machine learning algorithm that reduce deviations in expectation. However, existing machine learning and compensation frameworks cannot accommodate deviations of fully 3D shapes with different geometries. The feasibility of existing frameworks for geometric accuracy control is further limited by resource constraints in AM systems that prevent the printing of multiple copies of new shapes.<div><br></div><div>We present a closed-loop machine learning and compensation framework that can improve geometric accuracy control of 3D shapes in AM systems. Our framework is based on a Bayesian extreme learning machine (BELM) architecture that leverages data and deviation models from previously printed products to transfer deviation models, and more accurately capture deviation patterns, for new 3D products. The closed-loop nature of compensation under our framework, in which past compensated products that do not adequately meet dimensional specifications are fed into the BELMs to re-learn the deviation model, enables the identification of effective compensation plans and satisfies resource constraints by printing only one new shape at a time. The power and cost-effectiveness of our framework are demonstrated with two validation experiments that involve different geometries for a Markforged Metal X AM machine printing 17-4 PH stainless steel products. As demonstrated in our case studies, our framework can reduce shape inaccuracies by 30% to 60% (depending on a shape's geometric complexity) in at most two iterations, with three training shapes and one or two test shapes for a specific geometry involved across the iterations. We also perform an additional validation experiment using a third geometry to establish the capabilities of our framework for prospective shape deviation prediction of 3D shapes that have never been printed before. This third experiment indicates that choosing one suitable class of past products for prospective prediction and model transfer, instead of including all past printed products with different geometries, could be sufficient for obtaining deviation models with good predictive performance. Ultimately, our closed-loop machine learning and compensation framework provides an important step towards accurate and cost-efficient deviation modeling and compensation for fully 3D printed products using a minimal number of printed training and test shapes, and thereby can advance AM as a high-quality manufacturing paradigm.<br></div><div><br></div><div><b>2. Multiple Imputation and the Bootstrap for the Analysis of Big Data with Missingness</b></div><div><br></div><div>Inference can be a challenging task for Big Data. Two significant issues are that Big Data frequently exhibit complicated missing data patterns, and that the complex statistical models and machine learning algorithms typically used to analyze Big Data do not have convenient quantification of uncertainties for estimators. These two difficulties have previously been addressed using multiple imputation and the bootstrap, respectively. However, it is not clear how multiple imputation and bootstrap procedures can be effectively combined to perform statistical inferences on Big Data with missing values. We investigate a practical framework for the combination of multiple imputation and bootstrap methods. Our framework is based on two principles: distribution of multiple imputation and bootstrap calculations across parallel computational cores, and the quantification of sources of variability involved in bootstrap procedures that use subsampling techniques via random effects or hierarchical models. This framework effectively extends the scope of existing methods for multiple imputation and the bootstrap to a broad range of Big Data settings. We perform simulation studies for linear and logistic regression across Big Data settings with different rates of missingness to characterize the frequentist properties and computational efficiencies of the combinations of multiple imputation and the bootstrap. We further illustrate how effective combinations of multiple imputation and the bootstrap for Big Data analyses can be identified in practice by means of both the simulation studies and a case study on COVID infection status data. Ultimately, our investigation demonstrates how the flexible combination of multiple imputation and the bootstrap under our framework can enable valid statistical inferences in an effective manner for Big Data with missingness.<br></div>