Add hessian/fisher matrix for TweedieRegression

Internal feature

A prerequisite for several possible additional (Newton-like) solvers for TweedieRegression is the hessian or fisher matrix.

Issues/PR that depend on this

#16634, #16637, #16635

Discussion

Hessian vs Fisher

The Fisher information matrix is the expected hessian. It is always (semi-) positive definite (as it is the variance of the score). This has advantages for stability of solvers.

Full matrix vs diagonal part

The hessian and fisher matrix (without penalty) for GLMs has the following special structure X.T @ W @ X where W is a diagonal matrix (depending on the family, the link function and the coefficients/weights). Some solvers might prefer to get the whole matrix, others only the diagonal part W.

[rth]

I would would rather not include new solvers if they do not add significant values.

Not necessarily pushing for the addition of additional solvers aside for LBFGS, but having multiple solvers is useful to check that the implementation is correct. Here we can check it indirectly with Ridge and ElasticNet so it’s indeed less of a concern.

[rth]

For irls and newton_cg certainly. coordinate descent solver is still necessary if we want L1 penalty support irrespective of it’s performance compared to LBFGS…