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Sparse Recovery Problems in Machine Learning
Several methods of sparse recovery in empirical risk minimization
problems will be discussed. These methods are based on special
penalization techniques such as LASSO or l_1 penalization.
They can be used in a variety of problems of Machine Learning
such as regression and pattern classification and they provide
a way to find a sparse approximation of an unknown target function
and to reduce the dimensionality of the data. Recent attempts to
understand these problems mathematically are based on methods of asymptotic
geometric analysis and high dimensional probability.
The development of a theory and methods of sparse recovery
beyond the usual framework of finite dictionary to more
general settings of learning theory is a challenging open problem.