FIGURE 3.

Results of experiment 3, a comparison of the runtime of 10 steps of the approximate forward stepwise selection and standard forward stepwise procedure (left) and naïve lasso versus constrained lasso fitting (right). Fitting for forward stepwise selection and naïve lasso are done on the expanded feature set of all log-ratios, which is of size $\left(\begin{array}{c}\text{dimension}\\ 2\end{array}\right)$. Runtimes are from a Macbook pro with 3.3 GHz Intel Core i7 processor. Forward stepwise selection was fit using the leaps(Lumley, 2017) R package and lasso was fit with the glmnet(Friedman et al., 2010) R package. We note that glmnet is internally running FORTRAN code, which accounts for the large difference in runtime among the methods in the left versus right panels.