Model Free Prediction with Uncertainty Assessment
This addresses the problem of rigorous statistical inference for researchers in machine learning and statistics, offering a novel method for uncertainty assessment in deep learning.
The paper tackles the lack of asymptotic properties in deep nonparametric regression for statistical inference by proposing a framework using conditional diffusion models, resulting in established asymptotic normality and confidence regions validated through numerical experiments.
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.