generative models

[impossiblewizardry]

a regression model is not a generative model

a regression model, plus an estimated probability distribution for the features, is a generative model

But that's a generative model of (feature vector, response) pairs. If the features are generated from some underlying object, it's not a generative model of that object...

... unless you can invert the featurization process and find an objet with those features