Split Modeling for High-Dimensional Logistic Regression

A novel method is proposed to learn an ensemble of logistic classification models in the context of high-dimensional binary classification. The models in the ensemble are built simultaneously by optimizing a multi-convex objective function. To enforce diversity between the models the objective function penalizes overlap between the models in the ensemble. We study the bias and variance of the individual models as well as their correlation and discuss how our method learns the ensemble by exploiting the accuracy-diversity trade-off for ensemble models. In contrast to other ensembling approaches, the resulting ensemble model is fully interpretable as a logistic regression model and at the same time yields excellent prediction accuracy as demonstrated in an extensive simulation study and gene expression data applications. An open-source compiled software library implementing the proposed method is briefly discussed.

A robust and sparse K-means clustering algorithm

In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious and sometimes hard-to-assess problem for large and complex datasets. In this paper we show that a small proportion of atypical observations might have serious adverse effects on the solutions found by the sparse clustering algorithm of Witten and Tibshirani (2010). We propose a robustification of their sparse K-means algorithm based on the trimmed K-means algorithm of Cuesta-Albertos et al. (1997) Our proposal is also able to handle datasets with missing values. We illustrate the use of our method on microarray data for cancer patients where we are able to identify strong biological clusters with a much reduced number of genes. Our simulation studies show that, when there are outliers in the data, our robust sparse K-means algorithm performs better than other competing methods both in terms of the selection of features and also the identified clusters. This robust sparse K-means algorithm is implemented in the R package RSKC which is publicly available from the CRAN repository.