Year
2026
Authors
KLOPP Olga, DONNAT Claire, VERZELEN Nicolas
Abstract
A novel method is introduced for denoising partially observed signals over networks using graph total variation (TV) regularization, a technique adapted from signal processing to handle binary data. This approach extends existing results derived for Gaussian data to the discrete, binary case — a method hereafter referred to as “one-bit TV denoising.” The framework considers a network represented as a set of nodes with binary observations, where edges encode pairwise relationships between nodes. A key theoretical contribution is the establishment of consistency guarantees of graph TV denoising for the recovery of underlying node-level probabilities. The method is well suited for settings with missing data, enabling robust inference from incomplete observations. Extensive numerical experiments and real-world applications further highlight its effectiveness, underscoring its potential in various practical scenarios that require denoising and prediction on networks with binary-valued data. Finally, applications to two real-world epidemic scenarios demonstrate that one-bit total variation denoising significantly enhances the accuracy of network-based nowcasting and forecasting.
DONNAT, C., KLOPP, O. et VERZELEN, N. (2026). Denoising over networks with applications to partially observed epidemics. Computational Statistics and Data Analysis, 215, pp. 108276.