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

2024-09-23

AI Summary

Real-time estimation of the time-varying effective reproduction number (Rₜ) during the COVID-19 pandemic suffers from the absence of ground-truth labels and heavy reliance on empirical hyperparameter tuning. Method: We propose a ground-truth-free, data-driven framework based on a time-varying autoregressive Poisson (TV-AR-Poisson) model, integrating penalized likelihood estimation with a novel Stein’s Unbiased Risk Estimate (SURE) criterion. We extend Stein’s lemma to discrete-time Poisson settings and design a weekly-scale model to jointly account for infection stochasticity and reporting delay robustness. Contribution/Results: We theoretically establish the asymptotic unbiasedness of the SURE estimator. Extensive experiments on synthetic data validate its statistical efficacy, while application to real-world COVID-19 incidence data across multiple countries yields highly consistent, low-latency Rₜ trajectories. The framework significantly enhances model adaptability and practical deployability without requiring manual calibration or external validation labels.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

COVID-19 pandemic has brought to the fore epidemiological models which, though describing a wealth of behaviors, have previously received little attention in the 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, the 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 contamination while being robust to reporting errors. Finally, the overall data-driven procedure is particularized to the estimation of COVID-19 reproduction number demonstrating its ability to yield very consistent estimates.

Problem

• Estimating time-varying autoregressive model parameters accurately
• Selecting hyperparameters without ground truth for error minimization
• Improving COVID-19 reproduction number estimation robustness

Innovation

• Generalized time-varying autoregressive model for epidemics
• Penalized likelihood estimator for parameter estimation
• Data-driven oracles for hyperparameter selection