Model Free Prediction with Uncertainty Assessment

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.

CV: 康利灿，武汉大学武汉数学与智能研究院助理教授、研究员，主要研究方向包括深度学习、生成式学习、强化学习、科学智能、随机抽样算法和优化、非参数统计等领域。相关工作发表在包括Ann. Stat、Nat. Commun、J. Mach. Learn. Res、IEEE Trans. Inf. Theory、SIAM J.Control Optim、ICML等期刊和会议上。