Risk Estimate under a Time-Varying Autoregressive Model for Data-Driven Reproduction Number Estimation

TL;DR

This paper introduces a novel time-varying autoregressive model for estimating the COVID-19 reproduction number, utilizing data-driven hyperparameter tuning and risk estimation techniques, validated through simulations and real-world data.

Contribution

It develops a new risk estimation framework for a time-varying autoregressive Poisson model, incorporating hyperparameter selection and a robust weekly scaled Poisson model for epidemiological data.

Findings

Accurate reproduction number estimates from weekly COVID-19 data.

Effective hyperparameter tuning via data-driven oracles.

Robust modeling of infection variability and reporting errors.

Abstract

COVID-19 pandemic has brought to the fore epidemiological models which, though describing a wealth of behaviors, have previously received little attention in signal processing literature. In this work, a generalized time-varying autoregressive model is considered, encompassing, but not reducing to, a state-of-the-art model of viral epidemics propagation. The time-varying parameter of this model is estimated via the minimization of a penalized likelihood estimator. A major challenge is that the estimation accuracy strongly depends on hyperparameters fine-tuning. Without available ground truth, hyperparameters are selected by minimizing specifically designed data-driven oracles, used as proxy for the estimation error. Focusing on the time-varying autoregressive Poisson model, Stein's Unbiased Risk Estimate formalism is generalized to construct asymptotically unbiased risk estimators based on the derivation of an original autoregressive counterpart of Stein's lemma. The accuracy of these oracles and of the resulting estimates are assessed through intensive Monte Carlo simulations on synthetic data. Then, elaborating on recent epidemiological models, a novel weekly scaled Poisson model is proposed, better accounting for intrinsic variability of the contaminations while being robust to reporting errors. Finally, the data-driven procedure is particularized to the estimation of COVID-19 reproduction number from weekly infection counts demonstrating its ability to tackle real-world applications.