[WIP] Rational Quadratic Spline

[torfjelde]

EDIT: Realize I've needlessly started this branch from tor/couplings, so I'll close this PR and make a new one starting from master.

Implementation of Rational Quadratic Spline (RQS) [1] as a Bijector.

Notes

• At the moment RationalQuadraticSpline takes "unconstrained" parameters, i.e. expects input on ℝᵈ, despite the fact that under the hood we transform widths and heights to lie on a (d-1)-simplex S ⊂ ℝᵈ and derivatives to be positive. I initially didn't do this way, but instead let the user choose between passing the parameters wrapped in a Unconstrained struct, in which case we would perform the transformation, or as raw values, in which case it was assumed the parameters indeed was contained within their respective domains. I dropped the use of Unconstrained to reduce "new" code in this PR and since this is very similar to an issue we've expressed interest in solving in more generality.

TODOs

• Added Compat.jl as a requirement due to how much easier life becomes. That okay?
• Need to clean up parts of the implementation, e.g. batched multivariate impls.
• The way we currently do batching in forward for RQS is not the most efficient. So maybe drop the use of "merging" named tuples and instead implement "by hand" a batched version of forward.

References

1. Durkan, C., Bekasov, A., Murray, I., & Papamakarios, G., Neural Spline Flows, CoRR, arXiv:1906.04032 [stat.ML], (), (2019).

[torfjelde]

Closed in favour of #80