The classical binary classification problem is investigated
when it is known in advance that the posterior probability function
(or regression function) belongs to some class of functions. We introduce
and analyze a method which effectively exploits this knowledge. The method
is based on minimizing the empirical risk over a carefully selected
``skeleton'' of the class of regression functions. The skeleton is a
covering of the class based on a data--dependent metric, especially
fitted for classification. ...
The classical binary classification problem is investigated
when it is known in advance that the posterior probability function
(or regression function) belongs to some class of functions. We introduce
and analyze a method which effectively exploits this knowledge. The method
is based on minimizing the empirical risk over a carefully selected
``skeleton'' of the class of regression functions. The skeleton is a
covering of the class based on a data--dependent metric, especially
fitted for classification. A new scale--sensitive dimension is
introduced which is more useful for the studied classification problem
than other, previously defined, dimension measures. This fact is
demonstrated by performance bounds for the skeleton estimate in terms
of the new dimension.
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