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I have many phenomenons which I want to model them as lasso regression problem.

every phenomenon have it's own distinct features set. but for some phenomenons, the subset of features set are the same(shared), which define the relationship between these phenomenons.

I want to learn lasso models for all models at the same time, in such way that learning one model help to learn other model better. Does anyone have idea, how can I do this ? basically I want to have W(weights) as Matrix not as vector.

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