Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests

Understand

Normalizing flows have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction.

• We propose here an in-depth comparison of coupling and autoregressive flows, both based on symmetric (affine) and non-symmetric (rational quadratic spline) bijectors, considering four different architectures: real-valued non-Volume preserving (RealNVP), masked autoregressive flow (MAF), coupling rational quadratic spline (C-RQS), and autoregressive rational quadratic spline (A-RQS).
• We focus on a set of multimodal target distributions of increasing dimensionality ranging from 4 to 400.
• The performances were compared by means of different test statistics for two-sample tests, built from known distance measures: the sliced Wasserstein distance, the dimension-averaged one-dimensional Kolmogorov--Smirnov test, and the Frobenius norm of the difference between correlation matrices.