projection pursuit is network with one hidden layer that can be written asprojection pursuit (xs (ox)where is univariate smoothing cubic spline if we use squared-error loss with tn {yi xi }ni= we need to minimize the training loss  yi (oxi = with respect to and all cubic smoothing splines this training of the network is typically tackled iteratively in manner similar to the em algorithm in particularwe iterate ( the following steps until convergence (agiven the missing data ot compute the spline by training cubic smoothing spline on {yi > xi the smoothing coefficient of the spline may be determined as part of this step (bgiven the spline function compute the next projection vector ot+ via iterative reweighted least squaresot+ argmin (et xb)st (et xb) ( iterative reweighted least squares where yi ( > xi et, :ot xi ( > xi is the adjusted responseand / diag( ( > ) ( > xn )is diagonal matt rix apply taylor' theorem to the function and derive the iterative reweighted least-squares optimization program ( suppose that in the stochastic gradient descent method we wish to repeatedly draw minibatches of size from tn where we assume that for some large integer instead of repeatedly resampling from tn an alternative is to reshuffle tn via random permutation and then advance sequentially through the reshuffled training set to construct non-overlapping minibatches single traversal of such reshuffled training set is called an epoch the following pseudo-code describes the procedure epoch