Hai M. Nguyen | Searcharxiv

arXiv2025

An Error Model for Evaluating the Accuracy of Satellite-Based XCO$_2$ Products

Several satellites (e.g., OCO-2 & 3) and their derived products now provide spatially extensive coverage of the abundance of carbon dioxide in the atmospheric column (XCO$_2$). However, the accuracy of the XCO$_2$ reported in these products needs to be carefully assessed for any downstream scientific analysis; this involves comparison with reference datasets, such as those from the Total Carbon Column Observing Network (TCCON). Previously, systematic and random errors have been used to quantify differences between satellite-based XCO$_2$ measurements and TCCON data. The spatiotemporal density of satellite observations enables the decomposition of the error variability into these components. This study aims to unify the definitions of these error components through a hierarchical statistical model with explicit mathematical terms, which enables a formal definition of the underlying assumptions and estimation of each component. Specifically, we focus on defining model elements, like global bias and systematic and random error, as part of this framework. We use it to compare OCO-2 XCO$_2$ v11.1 data (both original scenes from the `Lite' files and 10-sec averages) and gridded Making Earth System Data Records for Use in Research Environments (MEaSUREs) products to TCCON data. The MEaSUREs products exhibit comparable systematic errors to other OCO-2 products, with larger errors over land versus ocean. We describe the methodology for creating the MEaSUREs products, including their prior and posterior error covariances, with information on spatial correlation for efficient incorporation into scientific analysis.

stat.AP↗

arXiv2023

Optimal Privacy Preserving for Federated Learning in Mobile Edge Computing

Federated Learning (FL) with quantization and deliberately added noise over wireless networks is a promising approach to preserve user differential privacy (DP) while reducing wireless resources. Specifically, an FL process can be fused with quantized Binomial mechanism-based updates contributed by multiple users. However, optimizing quantization parameters, communication resources (e.g., transmit power, bandwidth, and quantization bits), and the added noise to guarantee the DP requirement and performance of the learned FL model remains an open and challenging problem. This article aims to jointly optimize the quantization and Binomial mechanism parameters and communication resources to maximize the convergence rate under the constraints of the wireless network and DP requirement. To that end, we first derive a novel DP budget estimation of the FL with quantization/noise that is tighter than the state-of-the-art bound. We then provide a theoretical bound on the convergence rate. This theoretical bound is decomposed into two components, including the variance of the global gradient and the quadratic bias that can be minimized by optimizing the communication resources, and quantization/noise parameters. The resulting optimization turns out to be a Mixed-Integer Non-linear Programming (MINLP) problem. To tackle it, we first transform this MINLP problem into a new problem whose solutions are proved to be the optimal solutions of the original one. We then propose an approximate algorithm to solve the transformed problem with an arbitrary relative error guarantee. Extensive simulations show that under the same wireless resource constraints and DP protection requirements, the proposed approximate algorithm achieves an accuracy close to the accuracy of the conventional FL without quantization/noise. The results can achieve a higher convergence rate while preserving users' privacy.

cs.LG↗