  We consider a general statistical learning problem where an unknown fraction
of the training data is corrupted. We develop a robust learning method that
only requires specifying an upper bound on the corrupted data fraction. The
method minimizes a risk function defined by a non-parametric distribution with
unknown probability weights. We derive and analyse the optimal weights and show
how they provide robustness against corrupted data. Furthermore, we give a
computationally efficient coordinate descent algorithm to solve the risk
minimization problem. We demonstrate the wide range applicability of the
method, including regression, classification, unsupervised learning and classic
parameter estimation, with state-of-the-art performance.
