# [scikit-learn] Bounded logistical regression in Python

Joel Nothman joel.nothman at gmail.com
Thu Jan 31 05:48:43 EST 2019

```I don't quite get your terminology, to "add a variable c to center an
independent variable Xk", and you've got an extra ) in your equation, so
I'm not sure exactly where you want it... If you mean

P(X) = a / (1 + exp(b0 + b1*X1 + .. + bn*Xn) * (Xk  - c))

then that's the same as

P(X) = a / (1 + exp(b0 + b1*X1 + .. + bn*Xn + log(Xk)/log(c))

replace c by exp(1/bk) and you've got the same old logistic regression,
haven't you?

On Thu, 31 Jan 2019 at 20:53, Jaap van Kampen <jaapvankampen at gmail.com>
wrote:

> Hi there!
> The standard logistical regression solver
> <https://github.com/scikit-learn/scikit-learn/blob/7389dba/sklearn/linear_model/logistic.py#L998>
> in scikit-learn assumes the regression equation:<p>
> P(X) = 1/ (1 + exp(b0 + b1*X1 + ... + bn*Xn))</p>
> .. and solves for the b's using various solver routines.
>
> For a specific project, I'd like to bound the regression equation between
> 0-a (instead of 0-1) and add a variable c to center an independent variable
> Xk, e.g.<p>
> P(X) = a / (1 + exp(b0 + b1*X1 + .. + bn*Xn) * (Xk  - c)))  </p>
> ... and solve for a, b's and c.
>
> Any thoughts/ideas on how to modify logistic.py to achieve this? I thought
> of modifying the expit
> <https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.special.expit.html>function
> to reflect the changed equation. But how do a let the solvers know to also
> include the new variables a and c? Any scripts available that are able to
> handle my modified logistic regression equation?
>
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