We propose to use an optimal scoring procedure for classification, where LASSO estimation is incorporated. In the notation of the previous section, we wish to solve the following optimization problem. Minimize n−1∑i=1n{θ(gi)−XiTη}2+λ∑j=1p|ηj|(3) subject to the constraint N−1‖ZΘ‖2 = 1. Here is the outline for our procedure. Choose an initial score matrix Θ0 satisfying Θ0TDPΘ0=I, and let Θ0 = ZΘ.Fit a linear regression model of Θ0 on X subject to an L1 constraint on the parameters. Define the fitted values Θ0∗. Let f^(X) be the vector of fitted regression functions.Obtain the eigenvector matrix Φ of Θ0∗TΘ0 ; the optimal scores are Θ= Θ0Φ.Define fopt(x)=ΦTf^(x). Note that we are incorporating the LASSO estimation procedure in step (2) of the algorithm. We cannot use the algorithm of Tibshirani [11] because it is too computationally intensive for large p (number of genes). However, it turns out that the algorithm can be fit using standard software for SVMs, which we will now describe.
