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Systems such as “311” enable residents of a community to report on their environments and to request non-emergency municipal services. While such systems provide an important link between community and government, resident-generated data suffer from reporting bias, with some subpopulations reporting at lower rates than others. Our research focuses on defining the under-reporting of heating and hot water problems to New York City’s 311 system and developing methods to estimate under-reporting. First, we estimate non-reporting by fitting a latent variable model which estimates both the probability of an underlying heating problem conditional on building characteristics, and the probability of reporting a problem conditional on population characteristics. Second, we analyze “less-than-expected” reporting: buildings with fewer 311 calls than expected as compared to similarly-sized buildings with similar estimated problem durations. Together, these analyses determine neighborhoods and neighborhood-level socioeconomic characteristics that are predictive of under-reporting of heating and hot water problems. Our approaches can aid government agencies wishing to use resident-generated data to assist in constructing fair public policies. 

With an increased focus on incorporating fairness in machine learning models, it becomes imperative not only to assess and mitigate bias at each stage of the machine learning pipeline but also to understand the downstream impacts of bias across stages. Here we consider a general, but realistic, scenario in which a predictive model is learned from (potentially biased) training data, and model predictions are assessed post-hoc for fairness by some auditing method. We provide a theoretical analysis of how a specific form of data bias, differential sampling bias, propagates from the data stage to the prediction stage. Unlike prior work, we evaluate the downstream impacts of data biases quantitatively rather than qualitatively and prove theoretical guarantees for detection. Under reasonable assumptions, we quantify how the amount of bias in the model predictions varies as a function of the amount of differential sampling bias in the data, and at what point this bias becomes provably detectable by the auditor. Through experiments on two criminal justice datasets– the well-known COMPAS dataset and historical data from NYPD’s stop and frisk policy– we demonstrate that the theoretical results hold in practice even when our assumptions are relaxed. 

We propose a new approach, the calibrated nonparametric scan statistic (CNSS), for more accurate detection of anomalous patterns in large-scale, real-world graphs. Scan statistics identify connected subgraphs that are interesting or unexpected through maximization of a likelihood ratio statistic; in particular, nonparametric scan statistics (NPSSs) identify subgraphs with a higher than expected proportion of individually significant nodes. However, we show that recently proposed NPSS methods are miscalibrated, failing to account for the maximization of the statistic over the multiplicity of subgraphs. This results in both reduced detection power for subtle signals, and low precision of the detected subgraph even for stronger signals. Thus we develop a new statistical approach to recalibrate NPSSs, correctly adjusting for multiple hypothesis testing and taking the underlying graph structure into account. While the recalibration, based on randomization testing, is computationally expensive, we propose both an efficient (approximate) algorithm and new, closed-form lower bounds (on the expected maximum proportion of significant nodes for subgraphs of a given size, under the null hypothesis of no anomalous patterns). These advances, along with the integration of recent core-tree decomposition methods, enable CNSS to scale to large real-world graphs, with substantial improvement in the accuracy of detected subgraphs. Extensive experiments on both semi-synthetic and real-world datasets are demonstrated to validate the effectiveness of our proposed methods, in comparison with state-of-the-art counterparts. 

We generalize the spatial and subset scan statistics from the single to the multiple subset case. The two main approaches to defining the log-likelihood ratio statistic in the single subset case—the population-based and expectation-based scan statistics—are considered, leading to risk partitioning and multiple cluster detection scan statistics, respectively. We show that, for distributions in a separable exponential family, the risk partitioning scan statistic can be expressed as a scaled f-divergence of the normalized count and baseline vectors, and the multiple cluster detection scan statistic as a sum of scaled Bregman divergences. In either case, however, maximization of the scan statistic by exhaustive search over all partitionings of the data requires exponential time. To make this optimization computationally feasible, we prove sufficient conditions under which the optimal partitioning is guaranteed to be consecutive. This Consecutive Partitions Property generalizes the linear-time subset scanning property from two partitions (the detected subset and the remaining data elements) to the multiple partition case. While the number of consecutive partitionings of n elements into t partitions scales as O(n^(t−1)), making it computationally expensive for large t, we present a dynamic programming approach which identifies the optimal consecutive partitioning in O(n^2 t) time, thus allowing for the exact and efficient solution of large-scale risk partitioning and multiple cluster detection problems. Finally, we demonstrate the detection performance and practical utility of partition scan statistics using simulated and real-world data. Supplementary materials for this article are available online.