DAE 2024 - Session V

Session V (May 16, 8:30am-10:00am): Orthogonal arrays and related designs, organized by Boxin Tang

Title: Active Sampling for High-dimensional Ridge Estimator with Application in Genome-wide Association Studies
Speaker: Lin Wang, Purdue University
Abstract: Despite the availability of extensive data sets, it is often impractical to collect labels for all data points in many applications due to various measurement constraints. Subsampling approaches can be employed to select a subset of design points from a large pool, resulting in substantial savings in experimental costs. However, existing subsampling methods are primarily designed for low-dimensional data or rely on the assumption of sparse significant covariates. In this study, we propose a computationally tractable sampling method that enables the selection of a small subset from a large data set without assuming sparsity. Our method acknowledges the possibility that the number of significant covariates can be as large as or even larger than the sample size of the full data set. Specifically, our focus lies on ridge regression, for which we develop sampling probabilities that minimize the mean squared predictive risk on the full data set. The efficacy of our proposed approach is substantiated through theoretical analysis and extensive simulations. The results demonstrate its superiority over existing subsampling methods when dealing with high-dimensional data containing numerous significant covariates. Additionally, we illustrate the advantages of our new approach through its application to genome-wide association studies, highlighting its potential to yield valuable insights in this domain.

Title: Grouped Orthogonal Arrays
Speaker: Devon Lin, Queen's University
Abstract: We introduce a new class of arrays, called grouped orthogonal arrays, for computer experiments and statistical modeling to accommodate the case that there is the underlying functional form of the system or the statistical model to be used is additive where each component depends on one group of variables from a set of disjoint groups. We construct and study the newly introduced arrays. Many designs are tabulated for practical use. Compared with existing techniques in the literature, our construction methods can generate many more designs with flexible run sizes and better within-group projection properties for any prime power number of levels. This is joint work with Drs, Guanzhou Chen, Yuanzhen He, Fasheng Sun, and the PhD student Meixin Liu.

Title: Choosing Strength-Two Orthogonal Arrays that are Less Susceptible to Bias
Speaker: Bobby Mee, University of Tennessee
Abstract: We present two examples where prior information indicates that some isomorphic fractions are better than others. There are many applications where two isomorphic orthogonal arrays will have different susceptibilities to bias. Two-level orthogonal arrays of strength 2 that contain the all-low treatment combination or the all-high treatment combination can be shown to be more susceptible to bias for particular choices of factors or factor levels. Yet these fractions are generally the default fractions offered by design software. By reversing the levels of a subset of factors in the orthogonal array, we expect to obtain isomorphic fractions that produce main effect estimates with less bias and which lead the researcher to better and more accurate predictions.