通过定量回归建立生成模型

arXiv - STAT - Statistics Theory Pub Date : 2024-09-06 DOI:arxiv-2409.04231

Johannes Schmidt-Hieber, Petr Zamolodtchikov

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引用次数: 0

摘要

我们将条件生成模型与量子回归联系起来。我们提出了合适的损失函数，并推导出在条件分布的平滑性假设下相关风险的最小收敛率。为了确定下限，我们证明非参数回归可以看作是所考虑的生成建模框架的一个子问题。最后，我们讨论了从多元分布生成数据的工作扩展。

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Generative Modelling via Quantile Regression

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.

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arXiv - STAT - Statistics Theory

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