[论文解读] Coupling Power Laws Offers a Powerful Method for Problems such as Biodiversity and COVID-19 Fatality Predictions

Sam Ma|arXiv (Cornell University)|May 23, 2021

Data-Driven Disease Surveillance参考文献 28被引用 5

一句话总结

本文提出了一种新方法，将泰勒幂律（TPL）与带指数截断的幂律（PLEC）相结合，以改进对幂律现象（如生物多样性及新冠疫情死亡率拐点）的预测。通过整合TPL的方差估计与PLEC的渐近值预测，该方法为长期趋势提供了置信区间，在复杂且重尾的系统中显著提升了预测准确性。

ABSTRACT

Power laws have been found to describe a wide variety of natural (physical, biological, astronomic, meteorological, geological) and man-made (social, financial, computational) phenomena over a wide range of magnitudes, although their underlying mechanisms are not always clear. In statistics, power law distribution is often found to fit data exceptionally well when the normal (Gaussian) distribution fails. Nevertheless, predicting power law phenomena is notoriously difficult because some of its idiosyncratic properties such as lack of well-defined average value, and potentially unbounded variance. TPL (Taylor's power law), a power law first discovered to characterize the spatial and/or temporal distribution of biological populations and recently extended to describe the spatiotemporal heterogeneities (distributions) of human microbiomes and other natural and artificial systems such as fitness distribution in computational (artificial) intelligence. The power law with exponential cutoff (PLEC) is a variant of power-law function that tapers off the exponential growth of power-law function ultimately and can be particularly useful for certain predictive problems such as biodiversity estimation and turning-point prediction for COVID-19 infection/fatality. Here, we propose coupling (integration) of TPL and PLEC to offer improved prediction quality of certain power-law phenomena. The coupling takes advantages of variance prediction using TPL and the asymptote estimation using PLEC and delivers confidence interval for the asymptote. We demonstrate the integrated approach to the estimation of potential (dark) biodiversity and turning point of COVID-19 fatality. We expect this integrative approach should have wide applications given the duel relationship between power law and normal statistical distributions.

研究动机与目标

• 为解决预测高方差且数学期望未定义的幂律现象（如生物多样性和大流行病死亡率曲线）的挑战。
• 克服传统幂律模型在缺乏稳健渐近值估计和置信区间方面的局限性。
• 在统一框架中整合泰勒幂律（TPL）用于方差建模，以及带指数截断的幂律（PLEC）用于渐近值估计。
• 在现实应用中展示该方法的有效性，例如估算未被检测到的‘暗生物多样性’以及预测新冠疫情的拐点。

提出的方法

• 该方法将泰勒幂律（TPL）与种群分布的均值和方差关系建模相结合，以捕捉尺度相关的变异性。
• 整合带指数截断的幂律（PLEC），其可使幂律增长逐渐减弱，并实现对渐近饱和点的估计。
• 联合模型利用TPL估计数据的方差结构，利用PLEC建模增长的衰减，从而为预测的渐近值生成置信区间。
• 通过将耦合模型拟合到生物多样性计数和累计新冠疫情死亡人数的时间序列数据，来估计长期趋势。
• 该模型利用幂律的双重特性：通过TPL实现重尾行为，通过PLEC实现有界增长，从而提升鲁棒性。
• 通过统计推断推导预测渐近值周围的置信区间，增强决策的可靠性。

实验结果

研究问题

• RQ1 将TPL与PLEC耦合是否能提升对生物多样性及大流行病死亡率等幂律现象长期趋势的预测能力？
• RQ2 将方差估计（TPL）与渐近值预测（PLEC）相结合，相较于独立模型，如何增强对长期预测的置信度？
• RQ3 该耦合模型在多大程度上可估算因采样限制而未被检测到的‘暗’生物多样性？
• RQ4 该模型能否以可靠的置信区间准确预测新冠疫情死亡率曲线的拐点？
• RQ5 该双模型框架是否在捕捉现实世界数据中的变异性与饱和性方面，优于标准幂律或指数模型？

主要发现

• 耦合的TPL-PLEC模型成功估计了累计新冠疫情死亡人数的渐近值及其置信区间，从而实现了可靠的拐点预测。
• 该方法为渐近值提供了置信区间，相较于缺乏此类不确定性量化的标准幂律模型，具有显著改进。
• 该模型在利用TPL的方差匹配特性从稀疏采样数据外推估算潜在（‘暗’）生物多样性方面表现出色。
• TPL与PLEC的整合使预测结果比单独使用任一模型更加稳定和准确，尤其在具有重尾和饱和动力学的系统中表现更优。
• 该方法在真实世界数据上得到验证，表明耦合模型能够准确捕捉生物系统与大流行病系统中从加速增长到平台期的过渡。
• 该方法表明，当与截断机制结合时，具有无界方差的幂律现象可被可靠建模，为高斯假设提供了稳健的替代方案。