非光滑凸优化：在存在低质量数据的情况下稳健估计新冠病毒再生数的时空演变
Nonsmooth convex optimization to estimate the Covid-19 reproduction number space-time evolution with robustness against low quality data
AI总结：
研究旨在克服新冠病毒再生数估计对低质量数据缺乏稳健性的问题，通过精心设计泛函，联合估计再生数和异常值，增强正则性并保持凸性，设计高效算法，经理论证明和实际数据验证，还将实现估计值自动更新并公开开源程序。
摘要：
每日疫情监测对于国家卫生当局制定应对措施至关重要，通常通过估计再生数来实现。此前我们提出将再生数估计表述为一个优化问题，结合数据 - 模型保真度和时空正则性约束，通过非光滑凸近端最小化求解。但该方法对新冠病毒低质量数据缺乏稳健性。本工作旨在通过精心设计一个泛函来克服这些限制，该泛函能在一步中联合估计再生数和用于模拟低质量数据的异常值，同时增强再生数估计的流行病学驱动正则性属性并保持凸性，从而设计高效最小化算法。理论上证明了所提算法的显式收敛性，并在真实新冠病毒数据上量化了其相关性，还将通过动画和交互式地图报告估计值的每日自动更新，且开源估计程序将公开可用。
英文摘要：
Daily pandemic surveillance, often achieved through the estimation of the reproduction number, constitutes a critical challenge for national health authorities to design countermeasures. In an earlier work, we proposed to formulate the estimation of the reproduction number as an optimization problem, combining data-model fidelity and space-time regularity constraints, solved by nonsmooth convex proximal minimizations. Though promising, that first formulation significantly lacks robustness against the Covid-19 data low quality (irrelevant or missing counts, pseudo-seasonalities,.. .) stemming from the emergency and crisis context, which significantly impairs accurate pandemic evolution assessments. The present work aims to overcome these limitations by carefully crafting a functional permitting to estimate jointly, in a single step, the reproduction number and outliers defined to model low quality data. This functional also enforces epidemiology-driven regularity properties for the reproduction number estimates, while preserving convexity, thus permitting the design of efficient minimization algorithms, based on proximity operators that are derived analytically. The explicit convergence of the proposed algorithm is proven theoretically. Its relevance is quantified on real Covid-19 data, consisting of daily new infection counts for 200+ countries and for the 96 metropolitan France counties, publicly available at Johns Hopkins University and Sant{é}-Publique-France. The procedure permits automated daily updates of these estimates, reported via animated and interactive maps. Open-source estimation procedures will be made publicly available.
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