A0477
Title: Denoising data with measurement error using a reproducing kernel-based diffusion model
Authors: Ruoyu Wang - Harvard School of Public Health (United States) [presenting]
Mingyang Yi - Renmin University of China (China)
Marcos Matabuena - Harvard University (Spain)
Abstract: The ongoing technological revolution in measurement systems enables the acquisition of high-resolution samples in fields such as engineering, biology, and medicine. However, these observations are often subject to errors from measurement devices. Motivated by this challenge, a denoising framework that employs diffusion models is proposed to generate denoised data whose distribution closely approximates the unobservable, error-free data, thereby permitting standard data analysis based on the denoised data. The key element of the framework is a novel reproducing kernel Hilbert space-based method that trains the diffusion model with only error-contaminated data, admits a closed-form solution, and achieves a fast convergence rate in terms of estimation error. Furthermore, the effectiveness of the method is verified by deriving an upper bound on the Kullback-Leibler divergence between the distributions of the generated denoised data and the error-free data. A series of conducted simulations also verifies the promising empirical performance of the proposed method compared to other state-of-the-art methods. To further illustrate the potential of this denoising framework in a real-world application, it is applied in a digital health context, showing how measurement error in continuous glucose monitors can influence conclusions drawn from a clinical trial on diabetes Mellitus.
