American Scientist

At the University of California, Los Angeles, mathematician Andrea Bertozzi (below), a Sigma Xi Distinguished Lecturer, and anthropologist P. Jeffrey Brantingham (below) have teamed up to make mathematical models that can determine where crime is likely to occur in the near future. Their predictive policing software is already being used by several law enforcement departments to tailor the placement of police officers, potentially stopping crimes before they happen. They spoke about their research with managing editor Fenella Saunders. (See our companion blog post for a video of the full interview.)

What types of crimes do you model?

Bertozzi: We’re using statistical methods, and these methods work very well when you have a large population where you've got a number of different interacting players in the process: for example, residential burglaries, criminals interacting with the environment. Then we look at how one event might trigger another event. To date, we've mainly focused on crimes of opportunity and ones that happen fairly frequently.

Brantingham: It depends on the timescale. If you want to predict crimes on timescales of minutes to hours to maybe even days, you need very large populations. If you're talking about events like the shootings that happened in Orlando or at UCLA, it’s potentially possible to predict how many events like that are going to occur over the course of a year or maybe two years or five years, but not on a very short timescale of hours to days.

Is human behavior a factor?

Bertozzi: We're not tailing criminals and looking at how the criminals are making decisions. Rather, we're looking at actual patterns of events themselves and the location of the events. For example, if you have a house that's broken into, what happens in the general vicinity of that house? Does the probability of another break-in change at neighboring houses? It turns out that you can quantify those things very carefully. We’re much less focused on the individuals committing the crime than we are on the spatial targets of the crime.

Brantingham: In many cases, what’s driving where and when crime occurs is less dependent upon the motives of the offender than on the structure of the opportunities. That's why we can focus in on the events themselves rather than on the perpetrator and gain a lot of traction predicting where and when those crimes will occur.

Do other types of modeling relate to this problem?

Bertozzi: We looked at some models of microorganisms that change the environment around them and make it more hospitable, which causes aggregations to form. We also tapped into models related to earthquakes and their triggered aftershocks, which turn out to be wonderful statistical models for human activity.

What amount of data do you work with?

Brantingham: It depends on the timescale, but if you're looking at doing crime prediction on the order of days to maybe weeks within a particular region, you can gain some traction with hundreds of events. Most police departments, even relatively small ones, can find hundreds of events in their jurisdictions and start to use these models for prediction purposes.

What time frame and types of data do you use to build the model?

Brantingham: Typically, we look at years' worth of data in the background for predicting crime today. The process is an evolving one, not unlike Netflix. They have your entire movie-watching history in the background, and the movie you watch today changes the way the model appreciates how your tastes are evolving. In the same way we have lots of crime data going back years in the background, and the events that occur today change how we view the likelihood of crime occurring tomorrow.

The only data that we've really worked with over the long term is strictly the minimum of what you need to classify an event: We talk about what type of crime this is (a classification provided by the police department), where did it occur, and when did it occur—just those three things. You might say to yourself, “Well, what about street networks, and what about weather patterns, and what about demographic characteristics?” A lot of that stuff that we want to believe is really important for understanding crime actually is not nearly as important as we think it is. It's very difficult to figure out how do we actually use information about poverty or socioeconomic status as a component of models to forecast crime.

All of that additional information is already built into the events themselves. You can think of it as the event having already distilled all of those other variables in driving where and when it occurs. While it may be interesting to go out and map all of these other additional variables, it often doesn't provide you that much more information, and the costs of trying to gather those data and maintain them also becomes incredibly prohibitive.

Bertozzi: We have examples where the auxiliary data is really useful, but they tend to be special cases. One example is that for residential burglaries, we used census data of the population distribution in the city at a very fine scale. That's sort of obvious, that if you're talking about residential burglaries, you have to know where the residences are. Another type of auxiliary information we started looking at is graffiti when you have gang activity.

How do you address bias or privacy concerns?

Brantingham: We’re always concerned about those sorts of civil liberties issues that arise around this. We work with event data. Because we're only looking at the what, where, and when of the crimes themselves, it’s not actually about targeting people. It’s really about preventing crimes before they happen.

Bertozzi: Even with the few models we have that actually model the behavior of the criminals, we also assume the criminals are identical. They don't have a race, gender, or citizenship.

Is this program being used in police departments?

Bertozzi: The first use of our program started in the city of Santa Cruz. The first month they used this method, they had a 27 percent reduction in crime.

Brantingham: Based on that initial deployment of prototype software in Santa Cruz, we mounted a randomized, controlled experiment in Los Angeles that ran for 21 months. We were really trying to answer fundamental questions about science and crime. Within the first month or so, we received phone calls from more than 200 police departments asking for the software.

How do police departments get the data into the model for the next day’s predictions?

Brantingham: As the police add new crime events to their database, those automatically are incorporated into the predictions that are then delivered on an hourly or a daily basis to the police departments. It frees up time for them to concentrate on really challenging problems.

The predictive algorithm gives double the amount of crime that’s being predicted relative to a crime analyst. Where does this advantage come from? A really good analogy is if you were to name your top 20 favorite breakfast cereals in order. Numbers one, two, and three are easy. When you get to cereals four, five, and six it's a little bit harder. If you think about it, you get down to cereals 18, 19, and 20, and you’re making it up. You really do not know 20 breakfast cereals off the top of your head. Predicting crime is very similar.

Police departments don't need predictive policing to know where hot spots one, two, and three are. When you get to hot spots four, five, and six, on average, four is a little bit hotter than five, but today is it that way? If you go to six instead of four, maybe you miss an opportunity.

Then, if you get down to hot spots 18, 19, 20, you're making it up. The algorithm doesn't have that same limitation. It can look at every single event in the context of the complete history in space and time, and make a much more accurate call about, “This is hot spot 17 today,” or “This is hot spot 12 today.” In this context the algorithm has an advantage of being able to manage a much larger volume of data to pinpoint that risk.

What happens when dealing with hot spots causes them to shift locations?

Brantingham: When an area experiences a lot of crime, you put police on that hot spot, and oftentimes if you press down on that hot spot, the crime would just disappear. But sometimes, crime would displace around the corner.

These models provided one of the first early explanations for why you get these two different types of impacts of policing. If you have a system wherein any little spike in crime is sufficient to generate a new hot spot, if you push down on it, these little spikes in crime occur throughout the environment, and each one can become the nucleation point for a new hot spot.

In what we call subcritical environments, it really takes a big spike in crime to suck in all the offenders to that location to generate a new hot spot. If you push down on that type of hot spot, little spikes in crime aren't going to generate a new one. If you take away those attractive locations, oftentimes offenders will just go play XBox rather than go down around the corner and commit the crime. It’s a really nice formal mathematical description of the difference between supercritical and subcritical hot spots, providing a potential explanation for an empirical phenomenon that would not have been apparent without the mathematics.

People could turn around and say, “Yeah, but you’re not solving the root causes of crime. You're not solving drug addiction or poverty.” My answer to that is, its goal is not to solve those things. Those things are absolutely important, and we have to do something about those as a society. These sorts of methods are about giving the police officer on the street the ability to get out in front of crime today. I don't think we should be really thinking about either-or, preventing burglary today or solving poverty. We need to be thinking about both of those things simultaneously.

Could future models incorporate real-time data, such as from social media?

Bertozzi: We have a project under way right now looking at human terrain modeling. We're looking at what’s going on in urban environments and different parts of cities, and how much of this you can glean from social media activity. People who have a GPS tracker in a smartphone make a tweet that also records the geographic location of where the tweet came from. We're having some really interesting ongoing work in that area. But to date, our use of social media has not been focused on using it for crime. You get this broad brushstroke picture of what’s happening in the city that’s really quite fun to see, actually. We can take millions of tweets, and we can organize them into different categories, and then start combing through those in a very rapid fashion looking at different times of the year, and different locations, and what's going on. It's pretty exciting.

Brantingham: One of the things we’re looking at with social media data is the question of whether or not social media events themselves are embedded in people's daily routines, or does the social media drive their routine? There's a a bright future for using those sorts of data.