Dimension reduction strategies for modeling BI-clustered high dimensional data - Supranes, Michael Van B. (Quezon City University of the Philippines, 2016)
Abstract (A three-stage framework is developed for fitting a mixture of regressions for high dimensional data. The method combines a hierarchical agglomerative grouping algorithm, regression-based clustering, and a sequential, group-wise sparse estimation called Layered Elastic Net selection (LENS). A simulation study is used to compare the method with LASSO-typed and PC-based strategies in terms of predictive accuracy, selection optimality, and clustering accuracy. All simulation scenarios are high dimensional with varying correlation structures, and group-wise predictive contributions. When the group of most important predictors varies among regression components, the combination of OLS and the method using LENS outperforms LASSO-type and PC-based strategies in terms of predictions and clustering accuracy. Based on simulation, the method (termed as MixLENS) results to optimal variable selection, and applying OLS on selected variables results to better prediction and clusters. OLS-MixLENS may result to a more interpretable model that is as predictive as a full model (e.g. Mixture of PCRs). In general, MixLENS is likely to select an optimal small subset of predictors for modeling).
Thesis ( MS) --University of the Philippines