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A Simple Method to Evaluate Support Size and Non-uniformity of a Decoder-Based Generative Model

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Analysis of Images, Social Networks and Texts (AIST 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11832))

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Abstract

Theoretical analysis in [1] suggested that adversarially trained generative models are naturally inclined to learn distribution with low support. In particular, this effect is caused by the limited capacity of the discriminator network. To verify this claim, [2] proposed a statistical test based on the birthday paradox that partially confirmed the analysis. In this paper, we continue this line of work and develop a parameter-free and straightforward method to estimate the support size of an arbitrary decoder-based generative model. Our approach considers the decoder network from a geometric viewpoint and evaluates the support size as the volume of the manifold containing the generative model samples. Additionally, we propose a method to measure non-uniformity of a generative model that can provide additional insight into the model’s behavior. We then apply these tools to perform a quantitative comparison of common generative models.

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Notes

  1. 1.

    \(ReLU(x) = \max (0, x)\).

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Acknowledgements

The authors would like to thank Ilya Tolstikhin for fruitful discussions. The work was partly supported by Ministry of Education and Science of the Russian Federation (grant 14.756.31.0001). Dmitry Vetrov was also partly supported by Samsung Research, Samsung Electronics.

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Correspondence to Kirill Struminsky .

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Struminsky, K., Vetrov, D. (2019). A Simple Method to Evaluate Support Size and Non-uniformity of a Decoder-Based Generative Model. In: van der Aalst, W., et al. Analysis of Images, Social Networks and Texts. AIST 2019. Lecture Notes in Computer Science(), vol 11832. Springer, Cham. https://doi.org/10.1007/978-3-030-37334-4_8

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  • DOI: https://doi.org/10.1007/978-3-030-37334-4_8

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-37334-4

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