I have a logistic regression model and OLS estimation of its parameters $\hat{w}$: $$y=\sigma(x^Tw + b)$$
Now, I would like to reduce the dimensionality of the space in which $x \in X$ lies by some linear projection (e.g. obtained by a low-rank SVD). Therefore I obtain a linear projection matrix $P$ that I want to apply to my data $D\subseteq X$ to get the reduced dimensionality dataset: $$D'=PD$$
Is there a general way how to project $\hat w$ so that I don't need to re-estimate the model?
(The reason why I'm reducing the dimensions is to lower the computational cost of the subsequent computations that use D in a quadratic form)