Schedule for: 19w5101 - Mathematical Criminology and Security

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7:00am and 9:30am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Criminology over the past 100 years can be criticized in general for barely increasing our ability to explain crime. However, this general criticism glosses over significant differences between what Robert Merton identified as low-, middle and high-range theories. Low-range theories are can be described as 'empirical laws', while high-range theories are are grand unifying concepts. Middle-range theories are principles--perhaps law-like statements in themselves--that aggregate empirical laws and are subsumed by high-range theories. This paper surveys explanation at each of these levels and argues that we do quite well with explanation at the scale of empirical laws, but still struggle with grand unifying concepts. Mathematics has the greatest potential to contribute in framing middle-range theory, which we can hope will make high-range theory more tractable.

In this talk I will describe what agent-based models (ABMs) are and the mathematical challenges they present. I will also introduce data assimilation and the ensemble Kalman filter (EnKF). Using an extremely simple ABM, corresponding to a Markov chain that can be solved exactly, I will illustrate how the EnKF works and highlight some of things one must consider when applying data assimilation techniques. I will discuss an application using real data of footfall counts in Leeds.

Lunch is served daily between 12:00noon and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

We present a model to predict spatial hotspots, defined as the regions in a future time period that have the highest proportion of events of interest. We assume the conditional intensity of the events of interest can be influenced by geospatial and temporal predictors as well as nearby events from other point processes, a common assumption in crime and conflict processes. Likewise, our model explicitly incorporates the characteristics of the spatial environment, temporal trends, and estimates the influence of past events. As a variation on traditional self-exciting (Hawkes) point process models, we directly model the probability that a location will be a member of the hotspot in a future time period. We use a penalized logistic regression model that allows the spatial covariates and each event type to have a different effect (including inhibition) on the probability. The duration of an event's influence is modeled by a mixture of decay functions resulting in a flexible and interpretable dependence structure.

Crimes emerge out of complex interactions of behaviors and situations; thus there are complex linkages between crime incidents. Solving the puzzle of crime linkage is a highly challenging task because we often only have limited information from indirect observations such as records, text descriptions, and associated time and locations. We propose a new modeling and learning framework for detecting linkage between crime events using spatio-temporal-textual data, which are highly prevalent in the form of police reports. We capture the notion of modus operandi (M.O.), by introducing a multivariate marked point process and handling the complex text jointly with the time and location. The model is able to discover the latent space that links the crime series. The model fitting is achieved by a computationally efficient Expectation-Maximization (EM) algorithm. In addition, we explicitly reduce the bias in the text documents in our algorithm. Our numerical results using real data from the Atlanta Police show that our method has competitive performance relative to the state-of-the-art. Our results, including variable selection, are highly interpretable and may bring insights into M.O. extraction. This is a joint work with Shixiang Zhu at Georgia Tech.

We develop a sequential data assimilation algorithm for count data modelled by a doubly stochastic Poisson process. We apply an approximation technique similar to the extended Kalman filter to develop a sub-optimal discrete-time filtering algorithm, called the extended Poisson-Kalman lter (ExPKF), where only the mean and covariance are sequentially updated using count data via the Poisson likelihood function. The ExPKF, however, is inconvenient to use when the calculation of the Hessian is difficult. Thus, we also develop an ensemble-based filter based on the Gamma prior assumption; hence, ensemble Poisson-Gamma filter (EnPGF). The implementation of EnPGF is performed in the same manner as the serial-update version of EnKF. The performances of ExPKF and EnPGF are demonstrated in several synthetic experiments where the true solution is known. For the application to real-world data, we use ExPKF to approximate the uncertainty of urban crime intensity and parameters for Hawkes process and highlight the advantage of filtering scheme (over the non-filtering scheme) to track parameter changes.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Data science software has been abstracted to the point that a middle or high school student can implement an algorithm to forecast crime hotspots or predict recidivism (or classify images for that matter). The harder questions come after the modeling phase. Can police actually use these algorithms to reduce crime? How about "harm"? Are these algorithms fair or do they unfairly target certain groups? We have anonymous crime tips, is there an analogy to privacy preserving crime models? Should these algorithms be black boxes or should they be transparent and restricted in their inputs (like is done in insurance)? In this talk I will explore current research on these topics, highlighting some of our contributions and also gaps where further research is needed.

Applications such as police body-worn video cameras generate a huge amount of data, beyond what is humanly possible for analysts to review. Such problems are ripe for the development of semi-supervised learning algorithms, which, by definition, use a small amount of training data. We introduce an uncertainty quantification (UQ) method for graph-based semi-supervised multi-class classification problems. We not only predict the class label for each data point but also provide a confidence score for the prediction. We adopt a Bayesian approach and propose a graphical multi-class probit model together with an effective Gibbs sampling procedure. Furthermore, we propose a confidence measure for each data point that correlates with the classification performance. We use the empirical properties of the proposed confidence measure to guide the design of a human-in-the-loop system. The uncertainty quantification algorithm and the human-in-the-loop system are successfully applied to classification problems in image processing and ego-motion analysis of body-worn videos.

We investigate an SIRS epidemic PDE system with nonlinear incident rates. In the limit of small diffusion rate of infected class $D_I$, and on a finite interval, an equilibrium spike solution (or epidemic hotspot) to the epidemic model is constructed asymptotically and the motion of the spike is studied. For sufficiently large diffusion rate of recovered class $D_R$, the interior spike is shown to be stable, however it becomes unstable and moves to the boundary when $D_R$ is sufficiently small. We also studied two types of bifurcation behavior of multi-spike solutions: self-replication and spike competition, and their stability thresholds are precisely computed by asymptotic analysis and verified by numerical experiments. Finally, we show that the spike-type solution can transition into an interface-type solutions when the diffusion rates of recovered and susceptible class are sufficiently small, and the transition regime is obtained precisely.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Most approaches to the modelling of crime - for predictive purposes or otherwise - are situated in continuous space; most commonly continuous 2D space or a simple grid system. The true structure of urban space, however, is substantially more complex than this, with both the natural and built environment playing a key role in its configuration. A fundamental determinant of this structure is the street network, which governs both the locations of places and the paths between them. Empirical research has established not only that crime risk varies according to the structural (i.e. graph-theoretic) characteristics of streets, but that dynamic crime phenomena such as clustering can also be observed at the street network level. This evidence, as well as a number of conceptual concerns, suggests that the street network may constitute a more meaningful, or effective, substrate for models of crime. Initial research in this area using statistical models indeed suggests that the use of the street network can improve the predictive performance of crime models, producing outputs which can be readily acted upon by police forces. Nevertheless, there have been few attempts to use such representations of space in the context of more formal mathematical models. This talk will outline the state of evidence in this area, demonstrate some network-based approaches, and suggest opportunities for ongoing research.

Natural disasters have been posed a significant threat in many areas of the United States. Many catastrophic ones had taken the lives of millions of people throughout history and caused severe negative economic damages. For example, known as Hurricane Harvey, the tropical storm had brought the loss of more than 125 billion dollars in the U.S.A. in 2017. It also claimed at least 107 people’s lives during the period, displaced 30,000 people, and prompted more than 17,000 rescues [2]. However, some safety preparations can be made in advance to mitigate the potential damages and reduce the loss. Accurate prediction for natural disaster hotspots and timely rescue resource allocation are two primary precautions to send out the help before major destructive events strike the targeted area. Through monitoring the past events, we can strategically make the decision of where we should deploy the rescue team beforehand or announce an early evacuation warning. Such a prediction task can be considered as a reinforcement learning process while we make the decisions based on the reward from our past actions. We further formulate our decision-making problem as a multi-arm bandit (MAB) problem. We first consider every region in the disaster-stricken area as an arm of a multi-armed bandit machine. In every time period, by “pulling the arms,” we observe the number of the disaster events of interest in only a couple of regions and we decide the regions to be observed in the next time period based on the past limited observations. We propose a MAB strategy that considers the tradeoff between the exploration for overlooked places while exploiting the regions with high event intensity. Our strategy combines the traditional epsilon-greedy algorithm that allows us to probe the uncharted area with non-parametric Hawkes process to capture the temporal dynamics in those well-observed regions [4]. Several MAB algorithms are compared with our proposed model [3]. Specifically, we gather the dataset from city requests for service that is reported in Houston, Texas during the time period of tropical storm Harvey [1]. Flooding events are extracted as the natural disaster of interest. Our model and other baselines are further evaluated by the recall of flooding events throughout the recorded timespan of Hurricane Harvey. The proposed model has an improvement of 36.38% compared to the best baseline model. The improvement shows that our proposed model can not only exploit the best available options where there is a high probability of flooding, but it also can gather more information in those overlooked places. In our future work, more timely relevant information, such as tweets from Twitter and the water level record from observations nearby the river and ocean, will be integrated into our model to make predictions more accurate.

Compelling evidence now exists that collective efficacy - ‘social cohesion among neighbors combined with their willingness to intervene on behalf of the common good’ - plays an important role in shaping the patterning of crime, disorder, and perceptions of victimization risk across local areas. But existing studies have largely ignored the importance of consensus in residents’ assessments of collective efficacy. Yet there are good reasons to believe that this will also differ across neighborhood and, moreover, that such differences will be consequential for individual and community responses to crime and norm‐violating behaviour. Using data from a large random survey of London residents, I examine within‐neighborhood heterogeneity in collective efficacy ratings as a function of characteristics of not just neighborhoods but also the individual raters themselves. In addition to describing the patterning of consensus across and within neighborhoods, I also assess whether and how this heterogeneity shapes individual‐level fear of crime, risk avoidance behavior, and the experience of violent victimization.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.