Ploting the Lasso L1 constraint

Question

In Lasso regression the L1 constraint is used: $\lambda\sum_{j=1}^{p}\left | \beta_j \right |$

I'm trying to plot the constraint using R. An example looks like:

Here is the simple R code I wrote:

beta= seq(-1, 1, length=100)
lambda=2
penalty=lambda*abs(beta)
plot(penalty, type="l")

It draws only the lower part of the plot. How could I plot the upper part too in one plot? Here is the plot:

You're misunderstanding that plot. It's showing the equation abs(b1) + abs(b2) < 1 — IceCreamToucan, Jul 06 '18 at 17:57
if you just want to plot, you could use `polygon`, then you just need to pass the four corner coords — user20650, Jul 06 '18 at 18:00
@Ryan thank you, should then b1 be just an element of the vector B or a vector itself? — Ville, Jul 06 '18 at 18:02

score 2 · Accepted Answer · answered Jul 06 '18 at 18:12

2

To plot abs(b1) + abs(b2) = 1 you can plot b2 = 1 - abs(b1) and the negative of that (since the abs means either is a solution)

b1 <- seq(-1, 1, .01)
b2 <- 1 - abs(b1)
plot(b1, b2, ylim = c(-1, 1), type = 'l')
b2 <- -b2
lines(b1, b2)

answered Jul 06 '18 at 18:12

IceCreamToucan

thank you, this was exactly what I was trying to plot – Ville Jul 06 '18 at 18:18

1 Answers1