Predictive policing describes a collection of data-driven tools that are used to determine where to send officers on patrol on any given day. The idea behind these tools is that we can use historical data to make predictions about when and where crime will happen on a given day and use that information to allocate officers appropriately.

On the one hand, predictive policing tools are becoming ever more popular in jurisdictions across the country. They represent an argument based on efficiency: why not use data to model crime more effectively and therefore provision officers more usefully where they might be needed?

On the other hand, critiques of predictive policing point out that a) predicting crimes based on arrest data really predicts arrests and not crimes and b) by sending officers out based on predictions from a model and then using the resulting arrest data to update the model, you’re liable to get into a feedback loop where the model results start to diverge from reality.

This was empirically demonstrated quite elegantly by Lum and Isaac in a paper last year, using simulated drug arrest data in the Oakland area as well as an implementation of a predictive policing algorithm developed by PredPol (the implementation was based on a paper published by researchers associated with PredPol). For further discussion on this, it’s worth reading Bärí A. Williams’ op-ed in the New York Times, a response to this op-ed by Andrew Guthrie Ferguson (who’s also written a great book on this topic) and then a response by Isaac and Lum to his response.

Most of the discussion and response has focused on specifics of the kinds of crimes being recorded and modeled and the potential for racial bias in the outcomes.

In our work, we wanted to ask a more basic question: *what’s the mechanism that makes feedback affect the predictions a model makes*? The top-line ideas emerging from our work (two papers that will be published at the 1st FAT* conference and at ALT 2018) can be summarized as:

Biased observations can cause runaway feedback loops.If police don’t see crime in a neighborhoodbecause the model told them not to go there, this can cause a feedback loop.

Over time, such models can generate predictions of crime rates that (if used to decide officer deployment) will skew the data used to train the next iteration of the model. Since models might be run every day (and were done so in at least one published work describing PredPol-like algorithms), this skew might take hold quickly.

But this is still speculation. Can we **mathematically prove** that this will happen? The answer is yes, and this is the main contribution in our paper to appear at FAT*. By modeling the predictive process with a generalization of a Pólya urn, we can mathematically prove that the system will diverge out of control, to the extent that if two areas have even slightly different crime rates, a system that used predictive modeling to allocate officers, collect the resulting observational data and retrain the model will progressively put more and more emphasis on the area with the slightly higher crime rate.

Moreover, we can see this effect in simulations of real-world predictive policing deployments using the implementation of PredPol used by Lum and Isaac in their work, providing justification for our mathematical model.

Now let’s take a step back. If we have a model that exhibits runaway feedback loops, then we might try to fix the model to avoid such bad behavior. In our paper, we show how to do that as well. The intuition here is quite simple. Suppose we have an area with a very high crime rate as estimated by our predictive model. Then observing an incident should not *surprise* us very much: in fact, it’s likely that we shouldn’t even try to update the model from this incident. On the other hand, the less we expect crime to happen, the *more *we should be surprised by seeing an incident and the more willing we should be to update our model.

This intuition leads to a way in which we can take predictions produced by a black box model and tweak the data that is fed into it so that it only reacts to surprising events. This then provably yields a system that will converge to the observed crime rates. And we can validate this empirically again using the PredPol-inspired implementation. What our experiments show is that such a modified system does *not* exhibit runaway feedback loops.

A disclaimer: in the interest of clarity, I’ve conflated terms that in reality should be distinct: an incident is not an arrest is not a crime. And it can’t always be assumed that just because we don’t send an officer to an area that we don’t get any information about incidents (e.g via 911 calls). We model these issues more carefully in the paper, and in fact show that as the proportion of “reported incidents” (i.e those not obtained as a consequence of model-directed officer patrols) increases, model accuracy increases in a predictable and quantifiable way *if we assume that those reported incidents accurately reflect crime.* This is obviously a big assumption, and the extent to which different types of incidents reflect the underlying ground truth crime rate likely differs by crime and neighborhood – something we don’t investigate in our paper but believe should be a priority for any predictive policing system.

From the perspective of machine learning, the problem here is that the predictive system should be an online learning algorithm, but is actually running in batch mode. That means that it is unable to *explore* the space of possible models and instead merely *exploits* what it learns initially.

What if we could redesign the predictive model from scratch? Could we bring in insights from online learning to do a better job? This is the topic of our second paper and the next post. The short summary I’ll leave you with is that by carefully modeling the problem of limited feedback, we can harness powerful reinforcement learning frameworks to design new algorithms with provable bounds for predictive policing.