Hi David, Michael has great ideas and they might serve your purpose. If not and if you are willing to try another software package that is compatible with the scikit-learn ecosystem, you can look into pyglmnet:
http://glm-tools.github.io/pyglmnet/auto_examples/plot_tikhonov.html#sphx-glr-auto-examples-plot-tikhonov-py Hope this helps, Mainak On Tue, Aug 11, 2020 at 11:24 AM Michael Eickenberg < michael.eickenb...@gmail.com> wrote: > Hi David, > > I am assuming you mean that T acts on w. > If T is invertible, you can absorb it into the design matrix by making a > change of variable v=Tw, w=T^-1 v, and use standard ridge regression for v. > If it is not (e.g. when T is a standard finite difference derivative > operator) then this trick won't work. > A second thing you can do is to fit standard linear regression on the > augmented data matrix vstack([X, factor * T]) and the augmented target > concatenate([y, np.zeros(T.shape[0])]). > > At worst you can compute the gradient of your loss function X^T(Xw - y) + > T^Tw and perform gradient descent or compute w = (X^T X + T^T T)^{-1}X^T y. > > Hope this helps > > Michael > > On Mon, Aug 10, 2020 at 11:39 PM David Kleiven <davidkleiven...@gmail.com> > wrote: > >> Hi, >> >> I was looking at docs for Ridge regression and it states that it minimizes >> >> ||y - Xw||^2 + alpha*||w||^2 >> >> I would like to minimize the function >> >> ||y-Xw||^2 + ||Tx||^2, where T is a matrix, in order to impose certain >> properties on the solution vectors, but I haven't found any way to achieve >> that in scikit-learn. Is this type of regularisation supported in >> scikit-learn? >> >> More details on the ||Tx||^2 regularisation can be found here >> >> https://en.wikipedia.org/wiki/Tikhonov_regularization >> >> Best, >> David >> _______________________________________________ >> scikit-learn mailing list >> scikit-learn@python.org >> https://mail.python.org/mailman/listinfo/scikit-learn >> > _______________________________________________ > scikit-learn mailing list > scikit-learn@python.org > https://mail.python.org/mailman/listinfo/scikit-learn >
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