skglm
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Add datafit with log det datafit
Description of the feature
Handle $\log\det $-like datafit and allow variables with multiple roles.
Additional context
@bgirault-inria is currently solving (simpler) graphical-Lasso-like problems and could potentially benefit from our solvers.
The solved problem is $$\min_{w \in \mathbb{R}^p, q \in \mathbb{R}^m} \log \det (\mathrm{diag}(q) + \sum_e w_e b_e b_e^T) + A w + B q + \lambda \sum_e w_e + \sum_e i_{w_e \geq 0} + \sum_i i_{q_i \geq 0} $$
with given $A, B, b_e$.
This optimization problem raises two main challenges for our current implementation:
- the $\log \det $ derivative would require to store additional quantity for an efficient rank one update
- there are two variables $w$ and $q$, with 2 different roles.