An Efficient Quantile Spatial Scan Statistic for Finding Unusual Regions in Continuous Spatial Data with Covariates

Travis Moore, Weng-Keen Wong
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:755-764, 2018.

Abstract

Domains such as citizen science biodiversity monitoring and real estate sales are produc- ing spatial data with a continuous response and a vector of covariates associated with each spatial data point. A common data analy- sis task involves finding unusual regions that differ from the surrounding area. Existing techniques compare regions according to the means of their distributions to measure unusu- alness. Comparing means is not only vulner- able to outliers, but it is also restrictive as an analyst may want to compare other parts of the probability distributions. For instance, an analyst interested in unusual areas for high- end homes would be more interested in the 90th percentile of home sale prices than in the mean. We introduce the Quantile Spatial Scan Statistic (QSSS), which finds unusual regions in spatial data by comparing quantiles of data distributions while accounting for covariates at each data point. We also develop an exact in- cremental update of the hypothesis test used by the QSSS, which results in a massive speedup over a naive implementation.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-moore18a, title = {An Efficient Quantile Spatial Scan Statistic for Finding Unusual Regions in Continuous Spatial Data with Covariates}, author = {Moore, Travis and Wong, Weng-Keen}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {755--764}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/moore18a/moore18a.pdf}, url = {https://proceedings.mlr.press/r16/moore18a.html}, abstract = {Domains such as citizen science biodiversity monitoring and real estate sales are produc- ing spatial data with a continuous response and a vector of covariates associated with each spatial data point. A common data analy- sis task involves finding unusual regions that differ from the surrounding area. Existing techniques compare regions according to the means of their distributions to measure unusu- alness. Comparing means is not only vulner- able to outliers, but it is also restrictive as an analyst may want to compare other parts of the probability distributions. For instance, an analyst interested in unusual areas for high- end homes would be more interested in the 90th percentile of home sale prices than in the mean. We introduce the Quantile Spatial Scan Statistic (QSSS), which finds unusual regions in spatial data by comparing quantiles of data distributions while accounting for covariates at each data point. We also develop an exact in- cremental update of the hypothesis test used by the QSSS, which results in a massive speedup over a naive implementation.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T An Efficient Quantile Spatial Scan Statistic for Finding Unusual Regions in Continuous Spatial Data with Covariates %A Travis Moore %A Weng-Keen Wong %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-moore18a %I PMLR %P 755--764 %U https://proceedings.mlr.press/r16/moore18a.html %V R16 %X Domains such as citizen science biodiversity monitoring and real estate sales are produc- ing spatial data with a continuous response and a vector of covariates associated with each spatial data point. A common data analy- sis task involves finding unusual regions that differ from the surrounding area. Existing techniques compare regions according to the means of their distributions to measure unusu- alness. Comparing means is not only vulner- able to outliers, but it is also restrictive as an analyst may want to compare other parts of the probability distributions. For instance, an analyst interested in unusual areas for high- end homes would be more interested in the 90th percentile of home sale prices than in the mean. We introduce the Quantile Spatial Scan Statistic (QSSS), which finds unusual regions in spatial data by comparing quantiles of data distributions while accounting for covariates at each data point. We also develop an exact in- cremental update of the hypothesis test used by the QSSS, which results in a massive speedup over a naive implementation. %Z Reissued by PMLR on 04 October 2026.
APA
Moore, T. & Wong, W.. (2018). An Efficient Quantile Spatial Scan Statistic for Finding Unusual Regions in Continuous Spatial Data with Covariates. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:755-764 Available from https://proceedings.mlr.press/r16/moore18a.html. Reissued by PMLR on 04 October 2026.

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