Journal of Data Science

Bootstrapping is commonly used as a tool for non-parametric statistical inference to assess the quality of estimators in variable selection models. However, for a massive dataset, the computational requirement when using bootstrapping in variable selection models (BootVS) can be crucial. In this study, we propose a novel framework using a bag of little bootstraps variable selection (BLBVS) method with a ridge hybrid procedure to assess the quality of estimators in generalized linear models with a regularized term, such as lasso and group lasso penalties. The proposed method can be easily and naturally implemented with distributed computing, and thus has significant computational advantages for massive datasets. The simulation results show that our novel BLBVS method performs excellently in both accuracy and efficiency when compared with BootVS. Real data analyses including regression on a bike sharing dataset and classification of a lending club dataset are presented to illustrate the computational superiority of BLBVS in large-scale datasets.

Multi-classification is commonly encountered in data science practice, and it has broad applications in many areas such as biology, medicine, and engineering. Variable selection in multiclass problems is much more challenging than in binary classification or regression problems. In addition to estimating multiple discriminant functions for separating different classes, we need to decide which variables are important for each individual discriminant function as well as for the whole set of functions. In this paper, we address the multi-classification variable selection problem by proposing a new form of penalty, supSCAD, which first groups all the coefficients of the same variable associated with all the discriminant functions altogether and then imposes the SCAD penalty on the supnorm of each group. We apply the new penalty to both soft and hard classification and develop two new procedures: the supSCAD multinomial logistic regression and the supSCAD multi-category support vector machine. Our theoretical results show that, with a proper choice of the tuning parameter, the supSCAD multinomial logistic regression can identify the underlying sparse model consistently and enjoys oracle properties even when the dimension of predictors goes to infinity. Based on the local linear and quadratic approximation to the non-concave SCAD and nonlinear multinomial log-likelihood function, we show that the new procedures can be implemented efficiently by solving a series of linear or quadratic programming problems. Performance of the new methods is illustrated by simulation studies and real data analysis of the Small Round Blue Cell Tumors and the Semeion Handwritten Digit data sets.

Clustering is an essential technique for discovering patterns in data. Many clustering algorithms have been developed to tackle the ever increasing quantity and complexity of data, yet algorithms that can cluster data with mixed variables (continuous and categorical) remain limited despite the abundance of mixed-type data. Of the existing clustering methods for mixed data types, some posit unverifiable distributional assumptions or rest on unbalanced contributions of different variable types. To address these issues, we propose a two-step hybrid density- and partition-based (HyDaP) algorithm to detect clusters after variable selection. The first step involves both density-based and partition-based algorithms to identify the data structure formed by continuous variables and determine important variables (both continuous and categorical) for clustering. The second step involves a partition-based algorithm together with our proposed novel dissimilarity measure to obtain clustering results. Simulations across various scenarios were conducted to compare the HyDaP algorithm with other commonly used methods. Our HyDaP algorithm was applied to identify sepsis phenotypes and yielded important results.