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Robust Dimensionality Reduction: A Resistant Search for the Relevant Information in Complex Data
Abstract
With the increasing availability of massive data in various fields of applications such as engineering, economics, or biomedicine, there appears an urgent need for new reliable tools for obtaining relevant knowledge from such data, which allow one to find and interpret the most relevant features (variables). Such interpretation is however infeasible for the habitually used methods of machine learning, which can be characterized as black boxes. This chapter is devoted to variable selection methods for finding the most relevant variables for the given task. After explaining general principles, attention is paid to robust approaches, which are suitable for data contaminated by outlying values (outliers). Three main approaches to variable selection (prior, intrinsic, and posterior) are explained, and their recently proposed examples are illustrated on applications related to credit risk management and molecular genetics. These examples reveal recent robust approaches to data analysis to be able to outperform non-robust tools.
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