Ruben H. Zamar

Anthony-Alexander Christidis, Stefan Van Aelst, Ruben Zamar

Advances in data collecting technologies in genomics have significantly increased the need for tools designed to study the genetic basis of many diseases. Effective statistical methods should excel in both prediction accuracy and biomarker identification. We introduce a novel approach to high-dimensional binary classification that integrates regularization with ensembling techniques. The method constructs compact ensembles of interpretable models derived by optimizing a global objective function. In medical genomics applications, the proposed approach identifies critical biomarkers overlooked by competing methods. We develop a variable importance ranking system to help researchers prioritize promising genes. The method's asymptotic properties are established, and an efficient computational algorithm is provided. Through extensive simulations across complex scenarios and analysis of cancer genomics datasets, we demonstrate strong predictive performance. Based on the numerical experiments, we offer practical guidelines for determining optimal ensemble size.

Jakob Raymaekers, Ruben H. Zamar

We study a framework of regularized $K$-means methods based on direct penalization of the size of the cluster centers. Different penalization strategies are considered and compared through simulation and theoretical analysis. Based on the results, we propose HT $K$-means, which uses an $\ell_0$ penalty to induce sparsity in the variables. Different techniques for selecting the tuning parameter are discussed and compared. The proposed method stacks up favorably with the most popular regularized $K$-means methods in an extensive simulation study. Finally, HT $K$-means is applied to several real data examples. Graphical displays are presented and used in these examples to gain more insight into the datasets.

Hongyang Zhang, William J. Welch, Ruben H. Zamar

Tomal et al. (2015) introduced the notion of "phalanxes" in the context of rare-class detection in two-class classification problems. A phalanx is a subset of features that work well for classification tasks. In this paper, we propose a different class of phalanxes for application in regression settings. We define a "Regression Phalanx" - a subset of features that work well together for prediction. We propose a novel algorithm which automatically chooses Regression Phalanxes from high-dimensional data sets using hierarchical clustering and builds a prediction model for each phalanx for further ensembling. Through extensive simulation studies and several real-life applications in various areas (including drug discovery, chemical analysis of spectra data, microarray analysis and climate projections) we show that an ensemble of Regression Phalanxes improves prediction accuracy when combined with effective prediction methods like Lasso or Random Forests.

Jabed H Tomal, William J Welch, Ruben H Zamar

Two proteins are homologous if they have a common evolutionary origin, and the binary classification problem is to identify proteins in a candidate set that are homologous to a particular native protein. The feature (explanatory) variables available for classification are various measures of similarity of proteins. There are multiple classification problems of this type for different native proteins and their respective candidate sets. Homologous proteins are rare in a single candidate set, giving a highly unbalanced two-class problem. The goal is to rank proteins in a candidate set according to the probability of being homologous to the set's native protein. An ideal classifier will place all the homologous proteins at the head of such a list. Our approach uses an ensemble of models in a classifier and an ensemble of assessment metrics. For a given metric a classifier combines models, each based on a subset of the available feature variables which we call phalanxes. The proposed ensemble of phalanxes identifies strong and diverse subsets of feature variables. A second phase of ensembling aggregates classifiers based on diverse evaluation metrics. The overall result is called an ensemble of phalanxes and metrics. It provide robustness against both close and distant homologues.

Hongyang Zhang, Ruben H. Zamar

There has been a surge in the number of large and flat data sets - data sets containing a large number of features and a relatively small number of observations - due to the growing ability to collect and store information in medical research and other fields. Hierarchical clustering is a widely used clustering tool. In hierarchical clustering, large and flat data sets may allow for a better coverage of clustering features (features that help explain the true underlying clusters) but, such data sets usually include a large fraction of noise features (non-clustering features) that may hide the underlying clusters. Witten and Tibshirani (2010) proposed a sparse hierarchical clustering framework to cluster the observations using an adaptively chosen subset of the features, however, we show that this framework has some limitations when the data sets contain clustering features with complex structure. In this paper, we propose the Multi-rank sparse hierarchical clustering (MrSHC). We show that, using simulation studies and real data examples, MrSHC produces superior feature selection and clustering performance comparing to the classical (of-the-shelf) hierarchical clustering and the existing sparse hierarchical clustering framework.