One-Bit Total Variation Denoising over Networks with Applications to Partially Observed Epidemics

TL;DR

This paper develops a one-bit total variation denoising method for network-based epidemic modeling, providing theoretical guarantees and demonstrating improved accuracy in nowcasting and forecasting with incomplete data.

Contribution

It introduces a novel one-bit TV denoising approach for binary epidemic data, extending theoretical analysis to incomplete observations and real-world applications.

Findings

Proves consistency of graph-TV denoising for binary variables

Extends methodology to incomplete data scenarios

Demonstrates improved epidemic nowcasting and forecasting accuracy

Abstract

This paper introduces a novel approach for epidemic nowcasting and forecasting over networks using total variation (TV) denoising, a method inspired by classical signal processing techniques. Considering a network that models a population as a set of $n$ nodes characterized by their infection statuses $Y_i$ and that represents contacts as edges, we prove the consistency of graph-TV denoising for estimating the underlying infection probabilities $\{p_i\}_{ i \in \{1,\cdots, n\}}$ in the presence of Bernoulli noise. Our results provide an important extension of existing bounds derived in the Gaussian case to the study of binary variables -- an approach hereafter referred to as one-bit total variation denoising. The methodology is further extended to handle incomplete observations, thereby expanding its relevance to various real-world situations where observations over the full graph may not be accessible. Focusing on the context of epidemics, we establish that one-bit total variation denoising enhances both nowcasting and forecasting accuracy in networks, as further evidenced by comprehensive numerical experiments and two real-world examples. The contributions of this paper lie in its theoretical developments, particularly in addressing the incomplete data case, thereby paving the way for more precise epidemic modelling and enhanced surveillance strategies in practical settings.