Proposal

Remove the argument link from TweedieRegressor and always use a log-link.

Rationale

While PoissonRegressor and GammaRegressor have built-in log-link (prediction = exp(..)), the TweedieRegressor has an argument link : {'auto', 'identity', 'log'}, default='auto'.

The problem is that Tweedie should always predict positive vallues, but with link=identity`' this goes wrong, for example

import numpy as np
from sklearn.linear_model import TweedieRegressor


y = np.array([3, 2, 1, 0, 0])
X = np.arange(5)[:, None]
reg = TweedieRegressor(power=1, link='identity')  # power=1 optimizes Poisson deviance
reg.fit(X, y)
reg.predict(X)

Out[7]: array([ 1.95131702,  0.45263687, -1.04604328, -2.54472343, -4.04340359])

The only instance, where negatives predictions are ok, is power=0 which gives squared error. But if someone want't to fit squared error, she or he should better use Ridge and the likes.