notice how the approximation error becomes smaller as increases in this particular example the approximation error is in fact zero for in generalas the class of approximating functions becomes more complexthe approximation error goes down bthe nextwe illustrate the typical behavior of the statistical error since gt (xx> statistical error can be written as  ) ( [ - ]( du ( ( figure illustrates the decomposition ( of the generalization risk for the same training set that was used to compute the test loss in figure recall that test loss gives an estimate of the generalization riskusing independent test data comparing the two figureswe see that in this case the two match closely the global minimum of the statistical error is approximately with minimizer since the approximation error is monotonically decreasing to zerop is also the global minimizer of the generalization risk approximation error statistical error irreducible error generalization risk figure the generalization risk for particular training set is the sum of the irreducible errorthe approximation errorand the statistical error the approximation error decreases to zero as increaseswhereas the statistical error has tendency to increase after note that the statistical error depends on the estimate bwhich in its turn depends on the training set we can obtain better understanding of the statistical error by considering its expected behaviorthat isaveraged over many training sets this is explored in exercise using again squared-error lossa second decomposition (for general gstarts from `(ggt ``(ggt `( )where the statistical error and approximation error are combined using similar reasoning as in the proof of theorem we have  `(ggt (ggt (xy) ` ggt (xg( `ed (xt)