Abstract
In high-dimensional data, penalized regression is often used for variable selection and parameter estimation. However, these methods typically require time-consuming cross-validation methods to select tuning parameters and retain more false positives under high dimensionality. This chapter discusses sparse boosting based machine learning methods in the following high-dimensional problems. First, a sparse boosting method to select important biomarkers is studied for the right censored survival data with high-dimensional biomarkers. Then, a two-step sparse boosting method to carry out the variable selection and the model-based prediction is studied for the high-dimensional longitudinal observations measured repeatedly over time. Finally, a multi-step sparse boosting method to identify patient subgroups that exhibit different treatment effects is studied for the high-dimensional dense longitudinal observations. This chapter intends to solve the problem of how to improve the accuracy and calculation speed of variable selection and parameter estimation in high-dimensional data. It aims to expand the application scope of sparse boosting and develop new methods of high-dimensional survival analysis, longitudinal data analysis, and subgroup analysis, which has great application prospects.
Highlights
High-dimensional model has become very popular in statistical literature and many new machine learning techniques have been developed to deal with data with very large number of features
Variable selection is crucial to address the challenges. Regularization procedures such as LASSO [1], smoothly clipped absolute deviation (SCAD) [2], MCP [3] and their various extensions [4–6] have been thoroughly studied and widely used to perform variable selection and estimation simultaneously in order to improve the prediction accuracy and interpretability of the statistical model
In-sample prediction errors using L2 boosting is a little bit smaller than using sparse boosting since the former has lrargffiffiffieffiffirffiffiffimffiffiffiffioffiffiffidffiffieffiffiffilffiffisffiffiiffizffiffiffieffiffisffiffi,ffiffiffitffihffiffiffieffiffiffiaffiffiffivffiffieffiffirffiffiaffiffiffigffiffieffiffiffiffioffiffif root mean integrated squared errors using sparse boosting is much smaller than that using L2 boosting
Summary
High-dimensional model has become very popular in statistical literature and many new machine learning techniques have been developed to deal with data with very large number of features. Regularization procedures such as LASSO [1], smoothly clipped absolute deviation (SCAD) [2], MCP [3] and their various extensions [4–6] have been thoroughly studied and widely used to perform variable selection and estimation simultaneously in order to improve the prediction accuracy and interpretability of the statistical model. This chapter intends to solve the problem of how to improve the accuracy and calculation speed of variable selection and parameter estimation in high-dimensional data It aims to expand the application scope of sparse boosting and develop new methods of high-dimensional survival analysis, longitudinal data analysis, and subgroup analysis, which has great application prospects.
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