Confidence bounds for the generalization performances of linear combination of functions

This paper presents new results about confidence bounds on the generalization performances of linear combination of functions belonging to a set H. It is shown that when learning with monomial loss functions, the probability that the generalization error be greater than the empirical error plus ε, depends on the covering number of H and the magnitude of the coefficients of the combination. The classification case is studied by approximating a step function with polynomials