Alternative decision-making scenarios can be identified using mathematical model, study shows

Project can be applied to numerous areas, as well as helping managers create public policies.
Mathematics
04 January 2024
Alternative decision-making scenarios can be identified using mathematical model, study shows

If I paid off a certain debt, would I be able to get a bigger loan? If a neighborhood reduced the number of bus stops and invested in improving the socioeconomic conditions of the area, would it become safer? If I change the acidity of my soil and increase irrigation, can I increase my yields?

A study by Fundação Getulio Vargas’ School of Applied Mathematics (FGV EMAP), in conjunction with the University of Sao Paulo’s Institute of Mathematical and Computer Sciences, has developed a machine learning model capable of compiling numerous counterfactuals in order to find alternative contexts for making different types of decisions. “The applications of this theoretical model are wide ranging – there are no limitations,” says the study’s coordinator, Jorge Poco.

The professor says that in the set of various counterfactuals, i.e., alternative possibilities, a decision maker can opt for a more effective choice by understanding the different scenarios that each of these choices could entail. In addition, he points out that different areas of knowledge have their own models for finding alternative scenarios in their respective sectors. However, the model created by FGV EMAP can be applied to any area.

“Our model can be used in medicine, the financial sector, public security and many other areas. In addition, it is important to note that unlike other models, ours doesn’t just provide an alternative option, but a range of scenarios that can help different governments create public policies or help other researchers think about different ways of creating or applying a particular project,” Poco explains.

From theory to practice

The professor notes that the model, although theoretical, has countless possibilities for application. In fact, the project has already been applied by the Sao Paulo Municipal Public Security Secretariat in order to manage crime control, evaluating different counterfactuals that could improve security in some areas of the municipality.

“As a case study, we investigated crime patterns in the city of Sao Paulo, collecting socioeconomic, urban and crime information in census regions. Through a partnership with the University of Sao Paulo’s Center for Violence Studies, we gained access to criminal records, and through the same university’s Center for Metropolitan Studies, we obtained data on schools, bus stops and bars. With this information in hand, we classified the regions according to the rate of crimes committed by passers-by, normalized by the total population of each region,” Poco says.

The researchers then identified the places with the highest crime rates and, using a technique called regularized logistic regression, classified whether a given region was dangerous or not.

“Once a census region has been classified as dangerous, it is possible to create counterfactuals, i.e., alternative scenarios, which give an idea of what a decision maker could do to make that region safer. It is important to note that our models do not show a causal effect. This is because machine learning techniques are usually based on finding correlations between variables. However, our technique does show possible changes that could have an effect. It’s then up to decision makers to validate the results through additional experiments,” he says.

Pareto optimum

Researcher Marcos Raimundo of Campinas State University, who was also part of the project, believes that the solutions found by this system may vary according to the circumstances. The model finds these solutions through a concept called Pareto optimum. The aim is precisely to prevent the model from suggesting scenarios that are worse than those that have already been identified. From this principle came the title for this project, “Mining Pareto-optimal counterfactual antecedents with a branch-and-bound model-agnostic algorithm.”

Raimundo gives another example of the application of methodologies based on counterfactuals. “This type of methodology has already been applied to a project that evaluates truancy, mapping students’ socioeconomic attributes and academic performance. The intention was to understand alternative ways to try to reduce the number of students dropping out of school. In the same way, our system is able to demonstrate the conditions that could prevent truancy in the first place, such as the possibility of granting financial aid and changing the number of subjects or hours of study, among other things,” he says.

See the full study here.

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