# Relationship between LASSO T and LARS number of steps k

We can see on the figure (cf Least Angle Regression p30, Efron, Hastie, Johnstone, Tibshirani - link: Least Angle Regression) that there is a direct relationship between:

• LASSO T absolute norm of $\beta$: $T(\beta) = \sum_j\vert\beta_j\vert$
• and the number of steps $k$ computed by LARS.

I am trying to find a mathematical or at least a direct relationship between both LASSO T and LARS k, like $A = B$ or $A = x \Rightarrow B = f(x)$.

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 I don't see it on p30, can you you give the number of the equation? – Bitwise Oct 9 '12 at 16:17 It is the figure 8. (legend: Plot of S versus T...) p30. Actually, I guess that if you understand how he gets this number of points (number of LARS steps) and how they fit the whole LASSO curve, you should be able to explain the relationship between the number of steps k and the LASSO T absolute norm of beta (which is a bound actually). Thanks a lot for your help. – user1731029 Oct 9 '12 at 17:59 I've merged your accounts so you can edit your posts, comment under them and stuff. – mbq♦ Oct 9 '12 at 19:05