Evaluation of Penalized Estimation Methods for Big Data Analysis

Abstract

In this paper we described the sparse Laplacian shrinkage (SLS) method which is a penalized method for variable selection and estimation in big data analysis that uses a combination of the minimax concave penalty (MCP) and Laplacian quadratic as the penalty. The SLS uses the MCP to promote sparsity and Laplacian quadratic penalty to encourage smoothness among coefficients associated with the correlated predictors. An important advantage of the MCP over the penalty is that it leads to estimators that are nearly unbiased and achieve selection consistency under weaker conditions. In some problems such as genomic data analysis, partial external information may also be available on the graphical structure of some genes used as predictors in the model. It would be interesting to consider approaches for combining external information on the graphical structure with existing data in constructing the Laplacian quadratic penalty. We discussed a comparative study with ridge regression (Ridge), Lasso, MCP and SLS estimator. For different sample and variable size, our simulation studies demonstrate that SLS estimator is the best estimator.

Keywords: Big data, minimax concave penalty (MCP), sparse Laplacian shrinkage (SLS) estimator

Cite this Article

Rahman MS, Rahman MM, Matin MA. Evaluation of Penalized Estimation Methods for Big Data Analysis. Research & Reviews: A Journal of Bioinformatics. 2015; 2(2): 49–55p.