Edward McFowland

Scalable Detection of Anomalous Patterns With Connectivity Constraints

We present GraphScan, a novel method for detecting arbitrarily shaped connected clusters in graph or network data. Given a graph structure, data observed at each node, and a score function defining the anomalousness of a set of nodes, GraphScan can efficiently and exactly identify the most anomalous (highest-scoring) connected subgraph. Kulldorff’s spatial scan, which searches over circles consisting of a center location and its k − 1 nearest neighbors, has been extended to include connectivity constraints by FlexScan. However, FlexScan performs an exhaustive search over connected subsets and is computationally infeasible for k > 30. Alternatively, the upper level set (ULS) scan scales well to large graphs but is not guaranteed to find the highest-scoring subset. We demonstrate that GraphScan is able to scale to graphs an order of magnitude larger than FlexScan, while guaranteeing that the highest-scoring subgraph will be identified. We evaluate GraphScan, Kulldorff’s spatial scan (searching over circles) and ULS in two different settings of public health surveillance. The first examines detection power using simulated disease outbreaks injected into real-world Emergency Department data. GraphScan improved detection power by identifying connected, irregularly shaped spatial clusters while requiring less than 4.3 sec of computation time per day of data. The second scenario uses contaminant plumes spreading through a water distribution system to evaluate the spatial accuracy of the methods. GraphScan improved spatial accuracy using data generated from noisy, binary sensors in the network while requiring less than 0.22 sec of computation time per hour of data.

Penalized Fast Subset Scanning

We present the penalized fast subset scan (PFSS), a new and general framework for scalable and accurate pattern detection. PFSS enables exact and efficient identification of the most anomalous subsets of the data, as measured by a likelihood ratio scan statistic. However, PFSS also allows incorporation of prior information about each data element’s probability of inclusion, which was not previously possible within the subset scan framework. PFSS builds on two main results: first, we prove that a large class of likelihood ratio statistics satisfy a property that allows additional, element-specific penalty terms to be included while maintaining efficient computation. Second, we prove that the penalized statistic can be maximized exactly by evaluating only O(N) subsets. As a concrete example of the PFSS framework, we incorporate “soft” constraints on spatial proximity into the spatial event detection task, enabling more accurate detection of irregularly shaped spatial clusters of varying sparsity. To do so, we develop a distance-based penalty function that rewards spatial compactness and penalizes spatially dispersed clusters. This approach was evaluated on the task of detecting simulated anthrax bio-attacks, using real-world Emergency Department data from a major U.S. city. PFSS demonstrated increased detection power and spatial accuracy as compared to competing methods while maintaining efficient computation.

Efficient Discovery of Heterogeneous Treatment Effects in Randomized Experiments via Anomalous Pattern Detection

In the recent literature on estimating heterogeneous treatment effects, each proposed method makes its own set of restrictive assumptions about the intervention’s effects and which subpopulations to explicitly estimate. Moreover, the majority of the literature provides no mechanism to identify which subpopulations are the most affected–beyond manual inspection–and provides little guarantee on the correctness of the identified subpopulations. Therefore, we propose Treatment Effect Subset Scan (TESS), a new method for discovering which subpopulation in a randomized experiment is most significantly affected by a treatment. We frame this challenge as a pattern detection problem where we efficiently maximize a nonparametric scan statistic over subpopulations. Furthermore, we identify the subpopulation which experiences the largest distributional change as a result of the intervention, while making minimal assumptions about the intervention’s effects or the underlying data generating process. In addition to the algorithm, we demonstrate that the asymptotic Type I and II error can be controlled, and provide sufficient conditions for detection consistency–i.e., exact identification of the affected subpopulation. Finally, we validate the efficacy of the method by discovering heterogeneous treatment effects in simulations and in real-world data from a well-known program evaluation study.