Invertible Generative Modeling using Linear Rational Splines
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:42364246, 2020.
Abstract
Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in highdimensional scenarios. The first normalizing flow designs used coupling layer mappings built upon affine transformations. The significant advantage of such models is their easytocompute inverse. Nevertheless, making use of affine transformations may limit the expressiveness of such models. Recently, invertible piecewise polynomial functions as a replacement for affine transformations have attracted attention. However, these methods require solving a polynomial equation to calculate their inverse. In this paper, we explore using linear rational splines as a replacement for affine transformations used in coupling layers. Besides having a straightforward inverse, inference and generation have similar cost and architecture in this method. Moreover, simulation results demonstrate the competitiveness of this approach’s performance compared to existing methods.
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