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I am thinking about the possibility of making a parameter in my regression, let's say the $\lambda$ in a ridge regression, somehow, inside a range : $\lambda \in [0,1]$. Do you have any ideas how I can start ?

I oversimplified my problem, I am doing a regression with multiples criterions with parameters and I was wondering if I could make the regularization parameters preciser than just superior to zero. For now, I just look for a good tradeoff between different parameters and the least-squares.

${\displaystyle \min _{\beta }\,(\mathbf {y} -\mathbf {X} \beta )^{\mathsf {T}}(\mathbf {y} -\mathbf {X} \beta )+\lambda (\beta ^{\mathsf {T}}\beta -c)}$

Thank you

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  • $\begingroup$ You could use a convex Quadratic Programming (QP) solver, which allows linear constraints on the variables (such as $\lambda$). $\endgroup$
    – Mark L. Stone
    Commented May 9, 2022 at 15:53
  • $\begingroup$ Are you running a regression computationally or are you trying to find a closed-form solution? $\endgroup$
    – Scriddie
    Commented Jun 16, 2022 at 14:07

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