ENH: Add WeightedPoisson datafit with sample weights support

[Vrinda12-tech]

Summary

This PR adds a weighted variant of the Poisson datafit, enabling sample weights support for Poisson regression in skglm.

Implementation

• New class WeightedPoisson in skglm/datafits/single_task.py
• Follows the WeightedQuadratic pattern
• Numba JIT compiled for performance
• Sparse matrix support (CSC format)
• Numerical stability: np.clip(Xw, -500, 500) prevents exp overflow
• Safety floors in Lipschitz constants to prevent division by zero

Mathematical Derivation

The weighted Poisson loss is:

L = (1/Σw) * Σ( w_i * (exp((Xw)_i) - y_i * (Xw)_i) )

The weighted gradient:

∇L = (w * (exp(Xw) - y)) / Σw

The weighted Hessian:

H = (w * exp(Xw)) / Σw

Tests Added

• ✅ Equality with unweighted Poisson (equal weights)
• ✅ Correct scaling with arbitrary weights
• ✅ Zero weight handling
• ✅ Negative weight validation
• ✅ Sparse matrix support
• ✅ Lipschitz constant computation
• ✅ Integration with GeneralizedLinearEstimator

All 7 tests are passing locally.

References

• WeightedQuadratic implementation pattern
• Poisson datafit for unweighted version

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[mathurinm]

thanks a lot for the initiative !
There are lots of tests, do you think you could shorten them a bit for easier maintenance ? like factorize some aprts

also, can you have a single test where you have weights equal to 0, 1 or 2, and test that you get the same result as fitting with duplicated and removed samples (weights=2 or 0 respectively). I think this would remove the need for testing the lipschitz constant for example

[mathurinm]

you need spaces after the commas

[mathurinm]

this looks like a duplicate of what's 3 lines below

[mathurinm]

you can put the imports at the top of the file

[mathurinm]

@Badr-MOUFAD at some point I wonder if it wouldn't be easier if every datafit had weights by default... but not that much time to think about it

[Vrinda12-tech]

@mathurinm Thank you for the detailed review. I have addressed all the points:

1. Reduced the number of tests: I replaced test_weighted_poisson_equality, test_weighted_poisson_scaling, test_weighted_poisson_zero_weights, and test_weighted_poisson_lipschitz with a single duplication test (test_weighted_poisson_duplication).

2. The duplication test: It sets weights to 0 (remove), 2 (duplicate), and 1 (keep), then compares the weighted model against an unweighted model fit on the manually duplicated/removed dataset. This implicitly validates the loss, gradient, Hessian, and Lipschitz constants.

3. Alpha scaling: I initially tried to scale alpha for the unweighted model. I realized that because both losses are averaged (1/n for unweighted, 1/sum(w) for weighted), alpha should be identical for both models. The test now uses the same alpha and passes.

All 4 tests (duplication, validation, sparse, and integration) are passing locally.

Let me know if you have any other suggestions!