One Coordinate Drops Out - Lasso, Exactly

In a pinned independent-coordinate toy, the same lambda can leave one coordinate nonzero while another coordinate hits exact zero.

highlighted = computed this step

Choose one λ for both coordinates

Use a pinned independent-coordinate toy with λ=14. For these positive-source rows, each coordinate uses w_j=max(source_j minus λ, zero) divided by square_j. Lambda is chosen before the solve.

w_j={\max(\text{source}_j-\lambda,0)\over \text{square}_j},\quad \lambda=14

Feature A stays nonzero

Feature A has source sum 28 and square sum 14. Its numerator is max(28 minus 14, 0)=14, so its weight is 1 and the table marks it kept.

\max(28 - 14,0)=14\Rightarrow w_A=1

Feature B hits zero

Feature B has source sum 7 and the same square sum 14. Its numerator is max(7 minus 14, 0)=0, so its weight is 0 and the table marks it zeroed.

\max(7 - 14,0)=0\Rightarrow w_B=0

What this table says

The table is exactly these two displayed coordinates only. It shows L-one can hit exact zero when λ is chosen before the solve. It is NOT convergence, NOT general feature selection, NOT generalization, and NOT future-data proof.

\text{pinned independent-coordinate table only}