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December 2019 Scalable high-resolution forecasting of sparse spatiotemporal events with kernel methods: A winning solution to the NIJ “Real-Time Crime Forecasting Challenge”
Seth Flaxman, Michael Chirico, Pau Pereira, Charles Loeffler
Ann. Appl. Stat. 13(4): 2564-2585 (December 2019). DOI: 10.1214/19-AOAS1284

Abstract

We propose a generic spatiotemporal event forecasting method which we developed for the National Institute of Justice’s (NIJ) Real-Time Crime Forecasting Challenge (National Institute of Justice (2017)). Our method is a spatiotemporal forecasting model combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods for approximating Gaussian processes with autoregressive smoothing kernels in a regularized supervised learning framework. While the smoothing kernels capture the two main approaches in current use in the field of crime forecasting, kernel density estimation (KDE) and self-exciting point process (SEPP) models, the RKHS component of the model can be understood as an approximation to the popular log-Gaussian Cox Process model. For inference, we discretize the spatiotemporal point pattern and learn a log-intensity function using the Poisson likelihood and highly efficient gradient-based optimization methods. Model hyperparameters including quality of RKHS approximation, spatial and temporal kernel lengthscales, number of autoregressive lags and bandwidths for smoothing kernels as well as cell shape, size and rotation, were learned using cross validation. Resulting predictions significantly exceeded baseline KDE estimates and SEPP models for sparse events.

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Seth Flaxman. Michael Chirico. Pau Pereira. Charles Loeffler. "Scalable high-resolution forecasting of sparse spatiotemporal events with kernel methods: A winning solution to the NIJ “Real-Time Crime Forecasting Challenge”." Ann. Appl. Stat. 13 (4) 2564 - 2585, December 2019. https://doi.org/10.1214/19-AOAS1284

Information

Received: 1 July 2018; Revised: 1 July 2019; Published: December 2019
First available in Project Euclid: 28 November 2019

zbMATH: 07160950
MathSciNet: MR4037441
Digital Object Identifier: 10.1214/19-AOAS1284

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.13 • No. 4 • December 2019
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