figure two-dimensional uniform kdewith bandwidth the risk to minimize is thus `( : lossf ( ) ( ) (xg( )) dx we bypass the selection of class of approximation functions by choosing the learner to be specified by ( for fixed the objective is now to find that minimizes the generalization risk `(gt ( )or the expected generalization risk `(gt ( )the generalization risk is in this case (xgt ( )dx (xdx ( )gt ( sdx ( sdx minimizing this expression with respect to is equivalent to minimizing the last two termswhich can be written as xi ph - gt ( sdx = this expression in turn can be estimated by using test sample { xn from yielding the following minimization problemn xx xi ph dxgt (xi ph min = = = - xi - ph where ph - ph dx in the case of the gaussian kernel ( with to estimate in this way clearly requires test sampleor at least an application of cross-validation another approach is to minimize the expected generalization risk(that isaveraged over all training sets) (xgt ( )) dx this is called the mean integrated squared error (miseit can be decomposed into an integrated squared bias and integrated variance componentz (xegt ( )dx var(gt ( )dx mean integrated squared error