On the Regression Approach to Structured Output Regression ICML 2013 – SUPPLEMENTARY MATERIAL

In this supplementary material, we make use of the following notation. x i denotes the i th entry of the (column) vector X(x), y j the j th entry of the (column) vector Y (y), V[i; j] denotes the entry in position (i, j) of the matrix V. Also, V[ ; j] denotes the j th column of the matrix V. Finally, δ i,j denotes the delta function which gives 1 if i = j, and 0 otherwise. 7. Example of a distribution where the minimizer of the quadratic risk has a substantial higher error rate than the optimal classifier We consider a simple one-dimensional binary classification problem where X = R and Y = {−1, +1}. We thus consider classifiers identified by a single scalar weight w such that the output h w (x) on an input x is given by h w (x) = sgn(wx).