  We address the problem of general supervised learning when data can only be
accessed through an (indefinite) similarity function between data points.
Existing work on learning with indefinite kernels has concentrated solely on
binary/multi-class classification problems. We propose a model that is generic
enough to handle any supervised learning task and also subsumes the model
previously proposed for classification. We give a "goodness" criterion for
similarity functions w.r.t. a given supervised learning task and then adapt a
well-known landmarking technique to provide efficient algorithms for supervised
learning using "good" similarity functions. We demonstrate the effectiveness of
our model on three important super-vised learning problems: a) real-valued
regression, b) ordinal regression and c) ranking where we show that our method
guarantees bounded generalization error. Furthermore, for the case of
real-valued regression, we give a natural goodness definition that, when used
in conjunction with a recent result in sparse vector recovery, guarantees a
sparse predictor with bounded generalization error. Finally, we report results
of our learning algorithms on regression and ordinal regression tasks using
non-PSD similarity functions and demonstrate the effectiveness of our
algorithms, especially that of the sparse landmark selection algorithm that
achieves significantly higher accuracies than the baseline methods while
offering reduced computational costs.
