Optimization Techniques for SCAD Variable Selection in Medical Research
Journal Title: Biomedical Journal of Scientific & Technical Research (BJSTR) - Year 2018, Vol 8, Issue 2
Abstract
High-dimensional data analysis requires variable selection to identify truly relevant variables. More often it is done implicitly via regularization, such as penalized regression. Of the many versions of penalties, SCAD has shown good properties and has been widely adopted in medical research and many more areas. This paper reviews the various optimization techniques in solving SCAD penalized regression. High-dimensional data analysis has been a common and important topic in biomedical/genomic/clinical studies. For example, the identification of genetic factors for complex diseases such as lung cancer implicates a variety of genetic variants. For high-dimensional data, there is the well-known problem of curse of dimensionality arising in modeling. Therefore, variable selection is a fundamental task for high-dimensional statistical modeling. The "old school" way of doing variable selection is to follow a subset selection procedure prior to building the model of interest. The procedure commonly adopts AIC/BIC as evaluation metric and often iterates in a stepwise fashion. Yet this is independent of the subsequent modeling task hence the effectiveness might be less desirable. A more natural way is to integrate the variable selection into the modeling itself, i.e., the penalized regression, which simultaneously performs variable selection and coefficient estimation. Theoretically, the "best" penalty for the penalized regression is the number of non-zero variables, to push as many variables to zero as possible. Yet, it is well known that the L0 (also known as the entropy penalty) optimization [1] is infeasible. As such, the L1 (LASSO) penalty Tibshirani [2] is our "next best" candidate, which is widely adopted in statistical and machine learning community for sparse solutions. However, [3] point out that L1 suffers the problem of biasedness. They propose the Smoothly Clipped Absolute Deviation (SCAD) penalty that can produce unbiased estimates while retaining good properties of L1. Subsequently, the SCAD penalty function has seen a wide range of applications including medical/clinical research, such as [1,4-7]. Nevertheless, the estimating procedure for SCAD penalized regression is no trivial task, because the target function a) is a high-dimensional non-concave function, b) is singular at the origin, c) does not have continuous second order derivatives.
Authors and Affiliations
Yan Fang, Yan Yan Kong, Yumei Jiao
Keywords
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- EP ID EP585942
- DOI 10.26717/BJSTR.2018.08.001632
- Views 146
- Downloads 0
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