Additive Huber and generalization

[tommyod]

We could create an additive model that minimizes

$$f(g(X \beta) - y) + \alpha |P \beta|$$

where $g$ is the inverse link function as usual.
The function $f$ is usually $x \mapsto x^2$, but here we could use Huber, pseudohuber, or let the user subclass and define the function.

Instances of this loss function structure:

• Least squares (GAM with normal distribution)
• Huber regression
• Percentile regression (unsure about optimization of this...)
• Pseudo-huber
• $\ell_p$-norms