figure the generalization risk for fixed training set is the weighted-average loss over all possible pairs (xyexpected generalization risk for random training set the generalization risk is thus random variable that depends on (and gif we average the generalization risk over all possible instances of we obtain the expected generalization riske `(ggt loss(yggt ( ))( where (xyin the expectation above is independent of in the discrete casewe have `(ggt , , , ,xn ,yn loss(yggt ( ) (xyf ( (xn yn figure gives an illustration figure the expected generalization risk is the weighted-average loss over all possible pairs (xyand over all training sets for any outcome of the training datawe can estimate the generalization risk without bias by taking the sample average ` (ggt :test sample test loss loss(yi ggt ( )) = ( where {( )( yn )= is so-called test sample the test sample is completely separate from but is drawn in the same way as that isvia independent draws from (xy)for some sample size we call the estimator ( the test loss for random training set we can define ` (ggt similarly it is then crucial to assume that is independent of table summarizes the main definitions and notation for supervised learning