Neural Likelihoods via Cumulative Distribution Functions

Understand

We leverage neural networks as universal approximators of monotonic functions to build a parameterization of conditional cumulative distribution functions (CDFs).

• By the application of automatic differentiation with respect to response variables and then to parameters of this CDF representation, we are able to build black box CDF and density estimators.
• A suite of families is introduced as alternative constructions for the multivariate case.
• At one extreme, the simplest construction is a competitive density estimator against state-of-the-art deep learning methods, although it does not provide an easily computable representation of multivariate CDFs.