A visual model of Guy Bresler’s research would probably look like a Venn diagram. He works at the four-way intersection where theoretical computer science, statistics, probability, and information theory collide.

“There are always new things to do at the interface. There are always opportunities to ask entirely new questions,” says Bresler, an associate professor who recently landed a position in MIT’s Department of Electrical Engineering and Computer Science (EECS).

As a theoretician, he aims to understand the delicate interaction between the structure of the data, the complexity of the models and the amount of calculations required to learn these models. Recently, his main goal has been to uncover the fundamental phenomena that are largely responsible for determining the computational complexity of statistical problems – and to find the “sweet spot” where available data and computational resources allow researchers to efficiently solve a problem. problem.

When trying to solve a complex statistical problem, there is often a tug of war between data and computation. Without enough data, the computation needed to solve a statistical problem can be unsolvable, or at least consume a staggering amount of resources. But get just enough data and suddenly the unsolvable becomes solvable; the amount of computation needed to find a solution decreases dramatically.

The majority of modern statistical problems exhibit this type of computation-data trade-off, with applications ranging from drug development to weather forecasting. Another well-studied and practically important example is cryo-electron microscopy, says Bresler. With this technique, researchers use an electron microscope to take images of molecules in different orientations. The central challenge is how to solve the inverse problem – determining the structure of the molecule given the noisy data. Many statistical problems can be formulated as inverse problems of this type.

One of the aims of Bresler’s work is to elucidate the relationships between the wide variety of different statistical problems currently under study. The dream is to classify statistical problems into equivalence classes, as has been done for other types of computer problems in the field of computational complexity. Showing these kinds of relationships means that instead of trying to understand each problem in isolation, researchers can transfer their understanding from a well-studied problem to a poorly understood problem, he says.

**Take a theoretical approach**

For Bresler, a desire to theoretically understand various basic phenomena inspired him to follow a path to academia.

Both of his parents worked as teachers and showed how fulfilling academia can be, he says. His first introduction to the theoretical side of engineering came from his father, an electrical engineer and theorist studying signal processing. Bresler was inspired by his work from an early age. As an undergraduate at the University of Illinois at Urbana-Champaign, he bounced between physics, math, and computer science classes. But no matter the subject, he gravitated towards the theoretical point of view.

During his graduate studies at the University of California, Berkeley, Bresler had the opportunity to work on a wide variety of subjects spanning probability, theoretical computer science, and mathematics. His motivation was the love of learning new things.

“By working at the interface of multiple fields with new questions, you feel like you better learn as much as possible if you’re going to have a chance of finding the right tools to answer those questions,” he says. he.

This curiosity led him to MIT for a post-doctorate at the Laboratory for Information and Decision Systems (LIDS) in 2013, then he joined the faculty two years later as an assistant professor at the EECS, member of LIDS and a senior faculty member in the Institute for Data, Systems and Society (IDSS). He was appointed associate professor in 2019.

Bresler says he was drawn to the intellectual atmosphere at MIT, as well as the favorable environment for initiating bold research and trying to advance into new areas of study.

**Collaboration opportunities**

“What really struck me was how dynamic, energetic and collaborative MIT is. I have this mental list of 20+ people here that I would like to have lunch with each week and collaborate So just based on the numbers, joining MIT was a clear win,” he says.

He particularly enjoys collaborating with his students, who continually teach him new things and ask deep questions that fuel exciting research projects. One of those students, Matthew Brennan, who was one of Bresler’s closest aides, tragically and unexpectedly passed away in January 2021.

The shock of Brennan’s death is still raw for Bresler, and it derailed his research for a time.

“Beyond his prodigious abilities and creativity, he had this incredible ability to listen to an idea of mine that was almost completely wrong, extract a useful piece from it, and then pass the buck,” he says. “We had the same vision of what we wanted to accomplish in the job, and we were driven to try to tell a certain story. At the time, hardly anyone was pursuing that particular line of work, and it was kind of a kind of loneliness. But he trusted me and we encouraged each other to keep going when things looked bleak.

These lessons of perseverance fuel Bresler as he and his students continue to explore questions that, by their nature, are difficult to answer.

One area he has worked in intermittently for over a decade is learning graphical patterns from data. Models of certain types of data, such as time-series data consisting of temperature readings, are often built by experts in the field who have relevant knowledge and can construct a reasonable model, he explains.

But for many data types with complex dependencies, such as social networks or biological data, it’s not at all clear what structure a model should adopt. Bresler’s work aims to estimate a structured model from data, which could then be used for downstream applications like making recommendations or better predicting the weather.

The fundamental question of identifying good models, whether algorithmically in a complex setting or analytically, by specifying a useful toy model for theoretical analysis, connects abstract work to engineering practice, says -he.

“In general, modeling is an art. Real life is complicated, and if you write a super-complicated model that tries to capture all the features of a problem, it’s doomed to fail,” Bresler says. “You have to think about the problem and understand the practical side of things on some level to identify the correct features of the problem to model, so you can hope to actually solve it and get some insight into what to do in practice. ”

Outside the lab, Bresler often finds himself solving very different kinds of problems. He is an avid climber and spends much of his free time bouldering all over New England.

“I really like it. It’s a good excuse to go out and be sucked into a whole different world. Even though there’s problem solving and there are similarities on a philosophical level, it’s totally orthogonal to sitting down and doing math,” he says.