Robust normalizing flows using Bernstein-type polynomials

Sameera Ramasinghe (University of Adelaide),* Kasun Fernando (University of Toronto), Salman Khan (MBZUAI), Nick Barnes (ANU)
The 33rd British Machine Vision Conference


Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these initial errors, leading to poor generalizations. This paper proposes a framework to construct Normalizing Flows (NFs) which demonstrate higher robustness against such initial errors. To this end, we utilize Bernstein-type polynomials inspired by the optimal stability of the Bernstein basis. Further, compared to the existing NF frameworks, our method provides compelling advantages like theoretical upper bounds for the approximation error, better suitability for compactly supported densities, and the ability to employ higher degree polynomials without training instability. We conduct a theoretical analysis and empirically demonstrate the efficacy of the proposed technique using experiments on both real-world and synthetic datasets.



author    = {Sameera Ramasinghe and Kasun Fernando and Salman Khan and Nick Barnes},
title     = {Robust normalizing flows using Bernstein-type polynomials},
booktitle = {33rd British Machine Vision Conference 2022, {BMVC} 2022, London, UK, November 21-24, 2022},
publisher = {{BMVA} Press},
year      = {2022},
url       = {}

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