## Statistics, operations research, and better algorithms

In this day and age, many companies and institutions are not just data-driven, but data-intensive. Insurers, health providers, government agencies, and social media platforms are all heavily dependent on data-rich models and algorithms to identify the characteristics of the people who use them, and to nudge their behavior in various ways.

That doesn’t mean organizations are always using optimal models, however. Determining efficient algorithms is a research area of its own — and one where Rahul Mazumder happens to be a leading expert.

Mazumder, an associate professor in the MIT Sloan School of Management and an affiliate of the Operations Research Center, works both to expand the techniques of model-building and to refine models that apply to particular problems. His work pertains to a wealth of areas, including statistics and operations research, with applications in finance, health care, advertising, online recommendations, and more.

“There is engineering involved, there is science involved, there is implementation involved, there is theory involved, it’s at the junction of various disciplines,” says Mazumder, who is also affiliated with the Center for Statistics and Data Science and the MIT-IBM Watson AI Lab.

There is also a considerable amount of practical-minded judgment, logic, and common-sense decision-making at play, in order to bring the right techniques to bear on any individual task.

“Statistics is about having data coming from a physical system, or computers, or humans, and you want to make sense of the data,” Mazumder says. “And you make sense of it by building models because that gives some pattern to a dataset. But of course, there is a lot of subjectivity in that. So, there is subjectivity in statistics, but also mathematical rigor.”

Over roughly the last decade, Mazumder, often working with co-authors, has published about 40 peer-reviewed papers, won multiple academic awards, collaborated with major companies about their work, and helped advise graduate students. For his research and teaching, Mazumder was granted tenure by MIT last year.

From deep roots to new tools

Mazumder grew up in Kolkata, India, where his father was a professor at the Indian Statistical Institute and his mother was a schoolteacher. Mazumder received his undergraduate and master’s degrees from the Indian Statistical Institute as well, although without really focusing on the same areas as his father, whose work was in fluid mechanics.

For his doctoral work, Mazumder attended Stanford University, where he earned his PhD in 2012. After a year as a postdoc at MIT’s Operations Research Center, he joined the faculty at Columbia University, then moved to MIT in 2015.

While Mazumder’s work has many facets, his research portfolio does have notable central achievements. Mazumder has helped combine ideas from two branches of optimization to facilitate addressing computational problems in statistics. One of these branches, discrete optimization, uses discrete variables — integers — to find the best candidate among a finite set of options. This can relate to operational efficiency: What is the shortest route someone might take while making a designated set of stops? Convex optimization, on the other hand, encompasses an array of algorithms that can obtain the best solution for what Mazumder calls “nicely behaved” mathematical functions. They are typically applied to optimize continuous decisions in financial portfolio allocation and health care outcomes, among other things.

In some recent papers, such as “Fast best subset selection: Coordinate descent and local combinatorial optimization algorithms,” co-authored with Hussein Hazimeh and published in Operations Research in 2020, and in “Sparse regression at scale: branch-and-bound rooted in first-order optimization,” co-authored with Hazimeh and A. Saab and published in Mathematical Programming in 2022, Mazumder has found ways to combine ideas from the two branches.

“The tools and techniques we are using are new for the class of statistical problems because we are combining different developments in convex optimization and exploring that within discrete optimization,” Mazumder says.

As new as these tools are, however, Mazumder likes working on techniques that “have old roots,” as he puts it. The two types of optimization methods were considered less separate in the 1950s or 1960s, he says, then grew apart.

“I like to go back and see how things developed,” Mazumder says. “If I look back in history at [older] papers, it’s actually very fascinating. One thing was developed, another was developed, another was developed kind of independently, and after a while you see connections across them. If I go back, I see some parallels. And that actually helps in my thought process.”

Predictions and parsimony

Mazumder’s work is often aimed at simplifying the model or algorithm being applied to a problem. In some instances, bigger models would require enormous amounts of processing power, so simpler methods can provide equally good results while using fewer resources. In other cases — ranging from the finance and tech firms Mazumder has sometimes collaborated with — simpler models may work better by having fewer moving parts.

“There is a notion of parsimony involved,” Mazumder says. Genomic studies aim to find particularly influential genes; similarly, tech giants may benefit from simpler models of consumer behavior, not more complex ones, when they are recommending a movie to you.

Very often, Mazumder says, modeling “is a very large-scale prediction problem. But we don’t think all the features or attributes are going to be important. A small collection is going to be important. Why? Because if you think about movies, there are not really 20,000 different movies; there are genres of movies. If you look at individual users, there are hundreds of millions of users, but really they are grouped together into cliques. Can you capture the parsimony in a model?”

One part of his career that does not lend itself to parsimony, Mazumder feels, is crediting others. In conversation he emphasizes how grateful he is to his mentors in academia, and how much of his work is developed in concert with collaborators and, in particular, his students at MIT.

“I really, really like working with my students,” Mazumder says. “I perceive my students as my colleagues. Some of these problems, I thought they could not be solved, but then we just made it work. Of course, no method is perfect. But the fact we can use ideas from different areas in optimization with very deep roots, to address problems of core statistics and machine learning interest, is very exciting.”

Teaching and doing research at MIT, Mazumder says, allows him to push forward on difficult problems — while also being pushed along by the interest and work of others around him.

“MIT is a very vibrant community,” Mazumder says. “The thing I find really fascinating is, people here are very driven. They want to make a change in whatever area they are working in. And I also feel motivated to do this.” More