Add sum-of-squares polynomial flow

[François Rozet]

Description

The sum-of-squares polynomial flow is an interpretable and universal normalizing flow that was introduced in Sum-of-Squares Polynomial Flow (Jaini et al.). The idea is to model the first derivative of the transformations as the sum of squared polynomials, thereby enforcing monotonicity.

Implementation

The authors do not provide an official implementation. The transformation is not analytically invertible, but can be approximated using the bisection method if the features are bounded. The transformation could inherit from UnconstrainedMonotonicTransform.