Decision-makers often observe the occurrence of events through a reporting
process. City governments, for example, rely on resident reports to find and
then resolve urban infrastructural problems such as fallen street trees,
flooded basements, or rat infestations. Without additional assumptions, there
is no way to distinguish events that occur but are not reported from events
that truly did not occur--a fundamental problem in settings with
positive-unlabeled data. Because disparities in reporting rates correlate with
resident demographics, addressing incidents only on the basis of reports leads
to systematic neglect in neighborhoods that are less likely to report events.
We show how to overcome this challenge by leveraging the fact that events are
spatially correlated. Our framework uses a Bayesian spatial latent variable
model to infer event occurrence probabilities and applies it to storm-induced
flooding reports in New York City, further pooling results across multiple
storms. We show that a model accounting for under-reporting and spatial
correlation predicts future reports more accurately than other models, and
further induces a more equitable set of inspections: its allocations better
reflect the population and provide equitable service to non-white, less
traditionally educated, and lower-income residents. This finding reflects
heterogeneous reporting behavior learned by the model: reporting rates are
higher in Census tracts with higher populations, proportions of white
residents, and proportions of owner-occupied households. Our work lays the
groundwork for more equitable proactive government services, even with
disparate reporting behavior.

决策者通常通过报告过程观察事件的发生情况。在城市政府中，例如，依靠居民报告来发现并解决城市基础设施问题，例如树木倒塌、地下室涝水或鼠害问题。在正无标记数据的情况下，没有办法区分已发生但未被报告的事件和真正未发生的事件 - 这是存在基本难题。我们展示了如何充分利用事件的空间相关性来克服这一挑战。我们的框架利用贝叶斯空间潜变量模型推断事件发生的概率，并将其应用于纽约市风暴引发的洪水报告中，进一步汇总多个风暴的结果。我们展示了一个考虑少报告和空间相关性的模型比其他模型更准确地预测未来的报告，并进一步产生了更公平的检查分配：其分配更好地反映了人口情况并为非白人，较低教育水平和低收入居民提供公平的服务。我们的工作为更加公平的积极政府服务奠定了基础，即使报告行为存在差异。

一个贝叶斯空间模型用于纠正城市众包中的低报告

A Bayesian Spatial Model to Correct Under-Reporting in Urban  Crowdsourcing

We develop a classification algorithm for estimating posterior distributions
from positive-unlabeled data, that is robust to noise in the positive labels
and effective for high-dimensional data. In recent years, several algorithms
have been proposed to learn from positive-unlabeled data; however, many of
these contributions remain theoretical, performing poorly on real
high-dimensional data that is typically contaminated with noise. We build on
this previous work to develop two practical classification algorithms that
explicitly model the noise in the positive labels and utilize univariate
transforms built on discriminative classifiers. We prove that these univariate
transforms preserve the class prior, enabling estimation in the univariate
space and avoiding kernel density estimation for high-dimensional data. The
theoretical development and both parametric and nonparametric algorithms
proposed here constitutes an important step towards wide-spread use of robust
classification algorithms for positive-unlabeled data.

发展一种分类算法，可从正未标记数据中估计后验分布，对正标记上的噪声具有鲁棒性，对高维数据有效。