Model Free Prediction with Uncertainty Assessment

• URL: http://arxiv.org/abs/2405.12684v4
• Date: Wed, 31 Jul 2024 07:27:56 GMT
• Title: Model Free Prediction with Uncertainty Assessment
• Authors: Yuling Jiao, Lican Kang, Jin Liu, Heng Peng, Heng Zuo,
• Abstract summary: We propose a novel framework that transforms the deep estimation paradigm into a platform conducive to conditional mean estimation. We develop an end-to-end convergence rate for the conditional diffusion model and establish the normality of the generated samples. Through numerical experiments, we empirically validate the efficacy of our proposed methodology.
• Score: 7.524024486998338
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years. Despite considerable progress in understanding convergence rates, the absence of asymptotic properties hinders rigorous statistical inference. To address this gap, we propose a novel framework that transforms the deep estimation paradigm into a platform conducive to conditional mean estimation, leveraging the conditional diffusion model. Theoretically, we develop an end-to-end convergence rate for the conditional diffusion model and establish the asymptotic normality of the generated samples. Consequently, we are equipped to construct confidence regions, facilitating robust statistical inference. Furthermore, through numerical experiments, we empirically validate the efficacy of our proposed methodology.

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