美国低偏差高分辨率剥夺指数的数学构建
Mathematical construction of a low-bias high-resolution deprivation index for the United States
摘要：
贫困指数的构建由于贫困定义本身的模糊性以及党派操纵的可能性而变得复杂。然而，贫困指数为减轻贫困的影响和通过政策干预减少贫困提供了一个重要工具。在这里，我们展示了使用扩散图的剥夺指数的构建，扩散图是一种流形学习技术，能够找到最佳描述数据集中的变化的变量，在这个意义上保持数据点之间的成对关系。该方法适用于2010年美国十年一次的人口普查。与其他方法相比，所提出的程序并不从人口普查中选择特定的列，而是从完整的数据集中构建一个贫困指标。由于其结构，拟议的指数不引入偏见，除了那些已经存在于源数据，不需要规范的判断，某些生活方式的可取性，并对党派操纵的企图是高度弹性。我们证明，新的指数与既定的基于收入的剥夺指数，但偏离的方面，被认为是有问题的，在一些现有的指数。所提出的方法提供了一种有效的方法来构建准确的，高分辨率的指数。因此，这些指数有可能成为社会结构学术研究和政治决策的有力工具。
英文摘要：
The construction of deprivation indices is complicated by the inherent ambiguity in defining deprivation as well as the potential for partisan manipulation. Nevertheless, deprivation indices provide an essential tool for mitigating the effects of deprivation and reducing it through policy interventions. Here we demonstrate the construction of a deprivation index using diffusion maps, a manifold learning technique capable of finding the variables that optimally describe the variations in a dataset in the sense of preserving pairwise relationships among the data points. The method is applied to the 2010 US decennial census. In contrast to other methods the proposed procedure does not select particular columns from the census, but rather constructs an indicator of deprivation from the complete dataset. Due to its construction the proposed index does not introduce biases except those already present in the source data, does not require normative judgment regarding the desirability of certain life styles, and is highly resilient against attempts of partisan manipulation. We demonstrate that the new index aligns well with established income-based deprivation indices but deviates in aspects that are perceived as problematic in some of the existing indices. The proposed procedure provides an efficient way for constructing accurate, high resolution indices. These indices can thus have the potential to become powerful tools for the academic study of social structure as well as political decision making.
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