Hot-Spot Detection and Localization for Non-Stationary Poisson Count Tensor Data

Music City Center 

Count tensor data occur widely in many bio-surveillance and healthcare applications, e.g. the numbers of new patients of different types of infectious diseases from different cities/counties/states are collected repeatedly over time, say, daily/weekly/monthly. In this talk, we tackle the problem of quick detection and localization of hot-spots in terms of unusual infectious rates for count tensor data. Our main idea is as follow. First, we represent the observed count data as a three-dimensional tensor including (1) a spatial dimension for location patterns, e.g. different cities/countries/states; (2) a temporal domain for time patterns, e.g. daily/weekly/monthly; (3) a categorical dimension for different types of data sources, e.g. different types of diseases. Second, we fit this tensor data into a Poisson regression model with (non-stationary) smooth global trend, (sparse) local hot-spots, and (random) residuals. Third, we use sequential change-point detection methods to raise alarms when hot-spots occur, and discuss how to use LASSO-type methods to localize where hot-spots occur. The usefulness of our proposed methodology is validated through numerical simulation studies and a real-world dataset, which records the annual number of 10 different infectious diseases from 1993 to 2018 for 49 mainland states in the United States.

Hot-spot detection

Tensor data

Poisson Count

Change-point

LASSO

Statistical Process Control