Hi, thanks for your suggestions. I will try both options.
Best, David On Tue, Aug 11, 2020 at 5:39 PM Mainak Jas <mainak...@gmail.com> wrote: > 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 >> > _______________________________________________ > scikit-learn mailing list > scikit-learn@python.org > https://mail.python.org/mailman/listinfo/scikit-learn >
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