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I am taking a course about ridge, bridge and lasso regression. My teacher showed us that the solution to ridge regression can be written in the form

$$ \beta=(X^TX+\lambda I)^{-1}X^T Y $$

My question is do lasso and bridge regression have a similar solution?

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  • $\begingroup$ At least for LASSO this has been answered already in the site (albeit it's written in the question). $\endgroup$
    – Firebug
    Commented Nov 1, 2017 at 15:39
  • $\begingroup$ @Firebug, I have already checked that question before asking my question but I didn't understand what closed form lasso is and how it is related to lasso regression $\endgroup$
    – user3741635
    Commented Nov 1, 2017 at 15:53
  • $\begingroup$ It's written right at the beginning: $$\beta^{\text{lasso}}= \operatorname*{argmin}_\beta \| y-X\beta\|^2_2 + \alpha \| \beta\|_1$$ $\endgroup$
    – Firebug
    Commented Nov 1, 2017 at 16:04
  • $\begingroup$ At the end of the question is a demonstration why LASSO regression has no closed form solution (in fact some exist for special cases, like orthogonal dependent variables). $\endgroup$
    – Firebug
    Commented Nov 1, 2017 at 16:05
  • $\begingroup$ @Firebug That link doesn't demonstrate that lasso has no closed form solution: it just shows that the derivation attempted by OP is wrong. (I edited the title of the post last month since I saw someone else mistakenly reference it in the same way.) $\endgroup$
    – user795305
    Commented Nov 1, 2017 at 22:10

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