Rates of convergence for density estimation with generative adversarial networks
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866913207769104384 |
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| author | Puchkin, Nikita Samsonov, Sergey Belomestny, Denis Moulines, Eric Naumov, Alexey |
| author_facet | Puchkin, Nikita Samsonov, Sergey Belomestny, Denis Moulines, Eric Naumov, Alexey |
| contents | In this work we undertake a thorough study of the non-asymptotic properties of the vanilla generative adversarial networks (GANs). We prove an oracle inequality for the Jensen-Shannon (JS) divergence between the underlying density $\mathsf{p}^*$ and the GAN estimate with a significantly better statistical error term compared to the previously known results. The advantage of our bound becomes clear in application to nonparametric density estimation. We show that the JS-divergence between the GAN estimate and $\mathsf{p}^*$ decays as fast as $(\log{n}/n)^{2β/(2β+ d)}$, where $n$ is the sample size and $β$ determines the smoothness of $\mathsf{p}^*$. This rate of convergence coincides (up to logarithmic factors) with minimax optimal for the considered class of densities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_00199 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Rates of convergence for density estimation with generative adversarial networks Puchkin, Nikita Samsonov, Sergey Belomestny, Denis Moulines, Eric Naumov, Alexey Statistics Theory Machine Learning In this work we undertake a thorough study of the non-asymptotic properties of the vanilla generative adversarial networks (GANs). We prove an oracle inequality for the Jensen-Shannon (JS) divergence between the underlying density $\mathsf{p}^*$ and the GAN estimate with a significantly better statistical error term compared to the previously known results. The advantage of our bound becomes clear in application to nonparametric density estimation. We show that the JS-divergence between the GAN estimate and $\mathsf{p}^*$ decays as fast as $(\log{n}/n)^{2β/(2β+ d)}$, where $n$ is the sample size and $β$ determines the smoothness of $\mathsf{p}^*$. This rate of convergence coincides (up to logarithmic factors) with minimax optimal for the considered class of densities. |
| title | Rates of convergence for density estimation with generative adversarial networks |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2102.00199 |