通过联合字典学习和在线 NMF 进行 COVID-19 时间序列预测（CS LG）---刘持诚

预测 COVID-19 的传播和遏制，是当前广大科学界面临的一个极为重要的挑战。困难的主要原因之一是，每天可获得的 COVID-19 病例数据非常有限，除少数例外，大多数国家目前处于 "指数传播阶段"，因此，能够预测 COVID-19 传播和遏制之间的阶段性过渡的信息非常少。在本文中，我们提出了一种基于字典学习和在线非负矩阵因子化（online nonnegative matrix factorization）的预测 COVID-19 传播的新方法。其关键思想是同时学习多个国家的日新增病例的短时演化实例的字典模式，从而在字典模式中捕捉到它们的潜伏相关结构。我们首先通过从整个时间序列中的 minibatch 学习来训练这样的模式，然后通过在线 NMF 进一步适应时间序列。当我们逐步适应和改进所学的字典模式，以适应最近的观测结果时，我们还可以利用这些模式通过部分拟合来进行一步预测。最后，通过递归应用单步预测，我们可以将我们的预测结果推断到近期。我们的预测结果可以直接归功于被训练的字典模式，考虑到它们的可解释性。

原文题目：COVID-19 Time-series Prediction by Joint Dictionary Learning and Online NMF

原文：Predicting the spread and containment of COVID-19 is a challenge of utmost importance that the broader scientific community is currently facing. One of the main sources of difficulty is that a very limited amount of daily COVID-19 case data is available, and with few exceptions, the majority of countries are currently in the "exponential spread stage," and thus there is scarce information available which would enable one to predict the phase transition between spread and containment. In this paper, we propose a novel approach to predicting the spread of COVID-19 based on dictionary learning and online nonnegative matrix factorization (online NMF). The key idea is to learn dictionary patterns of short evolution instances of the new daily cases in multiple countries at the same time, so that their latent correlation structures are captured in the dictionary patterns. We first learn such patterns by minibatch learning from the entire time-series and then further adapt them to the time-series by online NMF. As we progressively adapt and improve the learned dictionary patterns to the more recent observations, we also use them to make one-step predictions by the partial fitting. Lastly, by recursively applying the one-step predictions, we can extrapolate our predictions into the near future. Our prediction results can be directly attributed to the learned dictionary patterns due to their interpretability.

原文作者：Hanbaek Lyu, Christopher Strohmeier, Georg Menz, Deanna Needell

原文地址：https://arxiv.org/abs/2004.09112