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Conceptually, I don't understand what least angle regression Least Angle Regression (LARS) is and why it solves LASSO (pdf).

We know that LASSO is:

$$\arg \min_x {\left\| A x - y \right\|}_{2}^{2} + \lambda {\left\| x \right\|}_{1}$$

From my understanding LARS is exactly like line search from CGD, where you take the variable that gives you the most desire result and iterate through.

Can someone give a walk through on how LARS solves LASSO?

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  • $\begingroup$ An edit request suggests that the LASSO be written as $\arg \min_x {\left\| A x - y \right\|}_{2}^{2} + \lambda {\left\| x \right\|}_{1}$ instead. But this should really be a comment rather than an edit, since fixing errors in someone else's equations is not really a job for the editing system $\endgroup$ – Silverfish Nov 21 '15 at 12:58
  • $\begingroup$ Why not? I'm interested in that question. It was formalized wrong the other time. Instead of opening new one, I fixed the errors here and hopefully someone would answer. There is no question here, the LASSO Problem is well defined. Moreover, it seems to be abandoned by the OP (He doesn't seem to be active anymore). $\endgroup$ – Royi Nov 21 '15 at 13:06
  • $\begingroup$ @Drazick It might be good to take that up in the meta thread Silverfish pointed to, perhaps in a comment to an answer you disagree with $\endgroup$ – Glen_b Nov 21 '15 at 14:55
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    $\begingroup$ have you read section 3.4.4 of ESL II? $\endgroup$ – MichaelChirico Feb 27 '18 at 6:02

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