Biomarker Identification Based on the L1 + L1 Penalized Model

Penalized feature selection and classification techniques are promising in bioinformatics studies of high-dimensional microarray data. The penalized objective function of penalization methods includes two parts: classification objective function and penalty terms. We propose a novel L₁ + L₁ model. The classification objective function is chosen as the negative log-likelihood function based on the posterior probability. To avoid the masking effect of the regression model that the penalized methods often focus on, the Bayes framework will be used to compute posterior probability after importing the Laplace distribution of the data. The Lasso penalty is imposed on the expectation of the distribution to achieve automatic feature selection. The experimental results from simulated data and acute leukemia cancer dataset show that our method is effective for selecting biologically meaningful discriminant genes and is useful for cancer diagnosis.