Algorithm 1.

Two-stage Log-ratio Lasso

1.	Fit the log-ratio lasso with tuning parameter λ.
2.	Using variables in the support from step one, enumerate all log-ratios into a matrix $\tilde{\mathbf{Z}}$.
3.	Use a sparse regression procedure to fit y onto $\tilde{\mathbf{Z}}$, with tuning paramemter γ.