Generative Modelling via Quantile Regression
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909307482669056 |
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| author | Schmidt-Hieber, Johannes Zamolodtchikov, Petr |
| author_facet | Schmidt-Hieber, Johannes Zamolodtchikov, Petr |
| contents | We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To establish the lower bound, we show that nonparametric regression can be seen as a sub-problem of the considered generative modelling framework. Finally, we discuss extensions of our work to generate data from multivariate distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generative Modelling via Quantile Regression Schmidt-Hieber, Johannes Zamolodtchikov, Petr Statistics Theory 62G08 (Primary), 62C20 (Secondary) We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To establish the lower bound, we show that nonparametric regression can be seen as a sub-problem of the considered generative modelling framework. Finally, we discuss extensions of our work to generate data from multivariate distributions. |
| title | Generative Modelling via Quantile Regression |
| topic | Statistics Theory 62G08 (Primary), 62C20 (Secondary) |
| url | https://arxiv.org/abs/2409.04231 |