Abstract: Normalizing flows (NFs) are a class of generative models that allows exact
density evaluation and sampling. We propose a framework to construct NFs based
on increasing triangular maps and Bernstein-type polynomials. Compared to the
existing (universal) NF frameworks, our method provides compelling advantages
like theoretical upper bounds for the approximation error, robustness, higher
interpretability, suitability for compactly supported densities, and the
ability to employ higher degree polynomials without training instability.
Moreover, we provide a constructive universality proof, which gives analytic
expressions of the approximations for known transformations. We conduct a
thorough theoretical analysis and empirically demonstrate the efficacy of the
proposed technique using experiments on both real-world and synthetic datasets.