Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using generalized Gini distance, an energy distance in reproducing kernel Hilbert spaces (RKHS). Two Gini distance based dependence measures are explored: Gini distance covariance and Gini distance correlation. Unlike Pearson covariance and correlation, which do not characterize independence, the above Gini distance based measures define dependence as well as independence of random variables. The test statistics are simple to calculate and do not require probability density estimation. Uniform convergence bounds and asymptotic bounds are derived for the test statistics. Comparisons with distance covariance statistics are provided. It is shown that Gini distance statistics converge faster than distance covariance statistics in the uniform convergence bounds, hence tighter upper bounds on both Type I and Type II errors. Moreover, the probability of Gini distance covariance statistic under-performing the distance covariance statistic in Type II error decreases to 0 exponentially with the increase of the sample size. Extensive experimental results are presented to demonstrate the performance of the proposed method.

Molecularly targeted therapies significantly contribute to the efforts of personalized approaches for cancer diagnosis and chemotherapeutic treatment. One of a critical step to identify target molecules is to determine the most representative features for different patient's sub-groups. Breast cancer, one of the most heterogeneous cancer has five main subtypes, so accurately identify gene signatures associated with intrinsic subtypes based on currently available data resource will benefit for precision medicine. Traditional ways to identify subtype-specific targeted molecular biomarkers are based on the platforms such as microarray, or immunohistochemistry (IHC) markers. Very few studies using RNAseq data to predict cancer subtype, due to the limited data resource. Gene expression in RNAseq platform is highly correlated with the microarray. However, it shows superior benefits than microarray in many ways, such as detection of low abundance transcripts, the broader dynamic range of gene expression in both coding and non-coding genes. Therefore, RNAseq platform will become the predominant tool for transcriptome analysis in the long term. To benefit the identification of molecule targets for transcriptomic data including RNAseq and microarray expression, we developed a new feature selection method. Our results of classification accuracy for intrinsic subtypes and prognostic evaluation of selected genes outperform than the traditional PAM50 gene signature, which is derived from microarray and widely used in clinical practice.