Spatio-temporal stochastic differential equations for crime incidence modeling

Abstract

We propose a methodology for the quantitative fitting and forecasting of real spatio-temporal crime data, based on stochastic differential equations. The analysis is focused on the city of Valencia, Spain, for which 90247 robberies and thefts with their latitude-longitude positions are available for a span of eleven years (2010–2020) from records of the 112-emergency phone. The incidents are placed in the 26 zip codes of the city (46001–46026), and monthly time series of crime are built for each of the zip codes. Their annual-trend components are modeled by Itô diffusion, with jointly correlated noises to account for district-level relations. In practice, this study may help simulate spatio-temporal situations and identify risky areas and periods from present and past data.

Cumulative Difference Learning VAE for Time-Series with Temporally Correlated Inflow-Outflow

“…For example, in the healthcare domain, while calibrating simulations requires patient flow attributes such as arrivals and departures, many datasets, such as COVID-19 hospitalization (Regenstrief Institute COVID-19 Dashboard 2023; WHO COVID-19 Dashboard 2023; CDC COVID-19 Tracking 2023), offer just the daily census. This unobservable issue is prevalent across different domains such as in social justice (Calatayud, Jornet, and Mateu 2023), traffic management (Dheeru and Karra Taniskidou 2017; Cuturi 2011), and energy conservation (Lai et al 2018a), making (iii) impractical to realize. Contrasting (iii), direct methods like ARIMA or RNN overlook the dependence between the observed data and the in-/outflow variables, missing the spatial-temporal correlations.…”

“…In the energy sector, X t signifies the observed energy volume at time t. This amount is driven by the newly collected energy A t and energy loss or consumption D t . X t for crime incidents can be interpreted similarly (Calatayud, Jornet, and Mateu 2023).…”

“…Existing methods fall short in addressing the challenges that arise in meeting this pressing demand, prompting the initiation of this research. Yet, these challenges are not unique to the healthcare domain; they are pervasive in many other applications such as crime prediction, financial trading, and traffic flow (Calatayud, Jornet, and Mateu 2023;Gontis, Ruseckas, and Kononovičius 2010;Tahmasbi and Hashemi 2014). The two primary challenges are (i) the errors tend to accumulate over time due to generation in an autoregressive/recursive manner (Yoon, Jarrett, and Van der Schaar 2019;Jeha et al 2021) and (ii) general-purpose (non-domain specific) generative methods often ignore problem structure and lack theoretical justification or interpretability.…”