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The selection of features that are relevant for a prediction or
classification problem is an important problem in many domains involving
high-dimensional data. Selecting features helps fighting the curse of
dimensionality, improving the performances of prediction or classification
methods, and interpreting the application. In a nonlinear context, themutual
information is widely used as relevance criterion for features and sets
of features. Nevertheless, it suffers from at least three major limitations:
mutual information estimators depend on smoothing parameters, there is
no theoretically justified stopping criterion in the feature selection greedy
procedure, and the estimation itself suffers from the curse of dimensionality.
This chapter shows how to deal with these problems. The two first
ones are addressed by using resampling techniques that provide a statistical
basis to select the estimator parameters and to stop the search procedure.
The third one is addressed by modifying the mutual information
criterion into a measure of how features are complementary (and not only
informative) for the problem at hand
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