Sparse Logistic Regression with Lp Penalty for Biomarker Identification

• Published in: Statistical Applications in Genetics and Molecular Biology Vol. 6; no. 1; pp. 6 - 27
• Main Authors: Liu, Zhenqiu, Jiang, Feng, Tian, Guoliang, Wang, Suna, Sato, Fumiaki, Meltzer, Stephen J., Tan, Ming
• Format: Journal Article
• Language: English
• Published: Germany bepress 10.02.2007; De Gruyter
• Subjects: Algorithms; Area Under Curve; Biomarkers - analysis; Colon - chemistry; Colonic Neoplasms - chemistry; Colonic Neoplasms - genetics; Esophageal Neoplasms - chemistry; Esophageal Neoplasms - genetics; feature selection; Gene Expression Profiling; Humans; Logistic Models; Lp penalty; microarry analysis; Oligonucleotide Array Sequence Analysis; sparse logistic regression
• ISSN: 1544-6115; 2194-6302; 1544-6115
• DOI: 10.2202/1544-6115.1248

In this paper, we propose a novel method for sparse logistic regression with non-convex regularization Lp (p <1). Based on smooth approximation, we develop several fast algorithms for learning the classifier that is applicable to high dimensional dataset such as gene expression. To the best of our knowledge, these are the first algorithms to perform sparse logistic regression with an Lp and elastic net (Le) penalty. The regularization parameters are decided through maximizing the area under the ROC curve (AUC) of the test data. Experimental results on methylation and microarray data attest the accuracy, sparsity, and efficiency of the proposed algorithms. Biomarkers identified with our methods are compared with that in the literature. Our computational results show that Lp Logistic regression (p <1) outperforms the L1 logistic regression and SCAD SVM. Software is available upon request from the first author.