An official website of the United States government
Predictive policing systems are increasingly used to determine how to allocate police across a city in order to best prevent crime. Discovered crime data (e.g., arrest counts) are used to help update the model, and the process is repeated. Such systems have been shown susceptible to runaway feedback loops, where police are repeatedly sent back to the same neighborhoods regardless of the true crime rate. In response, we develop a mathematical model of predictive policing that proves why this feedback loop occurs, show empirically that this model exhibits such problems, and demonstrate how to change the inputs to a predictive policing system (in a black-box manner) so the runaway feedback loop does not occur, allowing the true crime rate to be learned. Our results are quantitative: we can establish a link (in our model) between the degree to which runaway feedback causes problems and the disparity in crime rates between areas. Moreover, we can also demonstrate the way in which reported incidents of crime (those reported by residents) and discovered incidents of crime (i.e those directly observed by police officers dispatched as a result of the predictive policing algorithm) interact: in brief, while reported incidents can attenuate the degree of runaway feedback, they cannot entirely remove it without the interventions we suggest.
more »
« less
Beyond linearity, stability, and equilibrium: The edm package for empirical dynamic modeling and convergent cross-mapping in Stata
How can social and health researchers study complex dynamic systems that function in nonlinear and even chaotic ways? Common methods, such as experiments and equation-based models, may be ill-suited to this task. To address the limitations of existing methods and offer nonparametric tools for characterizing and testing causality in nonlinear dynamic systems, we introduce the edm command in Stata. This command implements three key empirical dynamic modeling (EDM) methods for time series and panel data: 1) simplex projection, which characterizes the dimensionality of a system and the degree to which it appears to function deterministically; 2) S-maps, which quantify the degree of nonlinearity in a system; and 3) convergent cross-mapping, which offers a nonparametric approach to modeling causal effects. We illustrate these methods using simulated data on daily Chicago temperature and crime, showing an effect of temperature on crime but not the reverse. We conclude by discussing how EDM allows checking the assumptions of traditional model-based methods, such as residual autocorrelation tests, and we advocate for EDM because it does not assume linearity, stability, or equilibrium.
more »
« less
- PAR ID:
- 10298676
- Date Published:
- Journal Name:
- The Stata Journal: Promoting communications on statistics and Stata
- Volume:
- 21
- Issue:
- 1
- ISSN:
- 1536-867X
- Page Range / eLocation ID:
- 220 to 258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Predictive policing systems are increasingly used to determine how to allocate police across a city in order to best prevent crime. Discovered crime data (e.g., arrest counts) are used to help update the model, and the process is repeated. Such systems have been empirically shown to be susceptible to runaway feedback loops, where police are repeatedly sent back to the same neighborhoods regardless of the true crime rate. In response, we develop a mathematical model of predictive policing that proves why this feedback loop occurs, show empirically that this model exhibits such problems, and demonstrate how to change the inputs to a predictive policing system (in a black-box manner) so the runaway feedback loop does not occur, allowing the true crime rate to be learned. Our results are quantitative: we can establish a link (in our model) between the degree to which runaway feedback causes problems and the disparity in crime rates between areas. Moreover, we can also demonstrate the way in which reported incidents of crime (those reported by residents) and discovered incidents of crime (i.e. those directly observed by police officers dispatched as a result of the predictive policing algorithm) interact: in brief, while reported incidents can attenuate the degree of runaway feedback, they cannot entirely remove it without the interventions we suggest.more » « less
-
In this work, we consider the problem of learning a reduced-order model of a high-dimensional stochastic nonlinear system with control inputs from noisy data. In particular, we develop a hybrid parametric/nonparametric model that learns the “average” linear dynamics in the data using dynamic mode decomposition with control (DMDc) and the nonlinearities and model uncertainties using Gaussian process (GP) regression and compare it with total least-squares dynamic mode decomposition (tlsDMD), extended here to systems with control inputs (tlsDMDc). The proposed approach is also compared with existing methods, such as DMDconly and GP-only models, in two tasks: controlling the stochastic nonlinear Stuart–Landau equation and predicting the flowfield induced by a jet-like body force field in a turbulent boundary layer using data from large-scale numerical simulations.more » « less
-
Abstract In this work, we consider the problem of learning a reduced-order model of a high-dimensional stochastic nonlinear system with control inputs from noisy data. In particular, we develop a hybrid parametric/nonparametric model that learns the “average” linear dynamics in the data using dynamic mode decomposition with control (DMDc) and the nonlinearities and model uncertainties using Gaussian process (GP) regression and compare it with total least-squares dynamic mode decomposition (tlsDMD), extended here to systems with control inputs (tlsDMDc). The proposed approach is also compared with existing methods, such as DMDc-only and GP-only models, in two tasks: controlling the stochastic nonlinear Stuart–Landau equation and predicting the flowfield induced by a jet-like body force field in a turbulent boundary layer using data from large-scale numerical simulations.more » « less
-
Abstract Methane dynamics within salt marshes are complex because vegetation types, temperature, oscillating water levels, and changes in salinity and redox conditions influence CH4production, consumption, oxidation, and emissions. These non‐linear and complex interactions among variables affect the traditionally expected functional relationships and present challenges for interpreting and developing process‐based models. We employed empirical dynamic modeling (EDM) and convergent cross mapping (CCM) as a novel approach for characterizing seasonal/multiday and diurnal CH4dynamics by inferring causal variables, lags, and interconnections among multiple biophysical variables within a temperate salt marsh using 5 years of eddy covariance data. EDM/CCM is a nonparametric approach capable of quantifying the coupling between variables while determining time scales where variable interactions are the most relevant. We found that gross primary productivity, tidal creek dissolved oxygen, and temperature were important for seasonal/multiday dynamics (rho = 0.73–0.80), while water level was most important for diurnal dynamics during both the growing and dormancy phenoperiods (rho = 0.72 and 0.56, respectively). Lags for the top‐ranked variables (i.e., gross primary productivity, dissolved oxygen, temperature, water level) occurred between 1 and 5 weeks at the seasonal scale and 1–24 hr at the diurnal scale. The EDM had high prediction capabilities for intra‐/inter‐seasonal patterns and annual CH4sums but had limitations in representing large, infrequent fluxes. Results highlight the importance of non‐linearity, drivers, lag times, and interconnections among multiple biophysical variables that regulate CH4fluxes in tidal wetlands. This research introduces a novel approach to examining CH4fluxes, which will aid in evaluating current paradigms in wetlands and other ecosystems.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1177/1536867X211000030
