The visual model of Jay Pressler’s research would likely look similar to a Venn diagram. It operates at the intersection of a quadrilateral where theoretical computer science, statistics, probability, and information theory collide.

“There is always new things to do on the front line. There are always opportunities to ask completely new questions,” says Pressler, an associate professor who recently held a position in the Department of Electrical Engineering and Computer Science (EECS) at MIT.

As a theorist, he aims to understand the precise interaction between structure in data, the complexity of models, and the amount of computation required to learn those models. Recently, his greatest focus has been to attempt to uncover the fundamental phenomena broadly responsible for determining the computational complexity of statistics problems – and to find the “sweet spot” where the available computational data and resources enable researchers to effectively solve a problem.

When trying to solve a complex statistical problem, there is often a tug of war between the data and the computation. Without enough data, the calculations needed to solve a statistical problem can be difficult to solve, or at least consume a huge amount of resources. But get enough data and suddenly the intractable becomes solvable; The amount of computations needed to come up with a solution drops dramatically.

The majority of recent statistical problems show this type of trade-off between computation and data, with applications ranging from drug development to weather forecasting. Another well-studied example of practical importance, Pressler says, is cryo-electron microscopy. With this technique, researchers use an electron microscope to take pictures of molecules in different directions. The central challenge is how to solve the inverse problem – determining the structure of a molecule in light of noisy data. Many statistical problems can be formulated as inverse problems of this type.

One of the goals of Bresler’s work is to elucidate the relationships between a variety of different statistical problems currently being studied. The dream is to classify statistical problems into equivalent classes, as happened with other types of computational problems in the field of computational complexity. Demonstrating these kinds of relationships means that instead of trying to understand each problem individually, researchers can move their understanding from a well-studied problem to a poorly understood one, he says.

**Adoption of the theoretical method**

For Pressler, the desire to theoretically understand various fundamental phenomena inspired him to follow a path into academia.

His parents worked as professors and showed how satisfying academia can be, he says. His first introduction to the theoretical side of engineering came from his father, an electrical engineer and theorist who studies 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, mathematics, and computer science courses. But regardless of the topic, he gravitated toward the theoretical point of view.

At the University of California, Berkeley Graduate School, Presler enjoyed the opportunity to work in a variety of subjects including probability, theoretical computer science, and mathematics. His motive was a love of learning new things.

“By working on the interface of multiple domains with new questions, there is a feeling that one would have learned as much as possible if one had any chance of finding the right tools to answer these questions,” he says.

This curiosity led him to the Massachusetts Institute of Technology for his Ph.D. in the Laboratory of Information Systems and Decision Making (LIDS) in 2013, and he joined the faculty two years later as an assistant professor at EECS. He was appointed associate professor in 2019.

Pressler says he was drawn to the intellectual atmosphere at MIT, as well as the supportive environment for launching bold research missions and trying to make headway in new areas of study.

**Cooperation Opportunities**

“What really surprised me is how vibrant, active and collaborative MIT is. I have this mental list of over 20 people here that I would like to lunch with every week and collaborate with on research. So, judging by the sheer numbers, joining MIT was a clear win.”

He particularly enjoyed collaborating with his students, who constantly teach him new things and ask deep questions that drive exciting research projects. One of these students, Matthew Brennan, who was one of Pressler’s closest collaborators, tragically and unexpectedly Passed away In January 2021.

The shock of Brennan’s death is still cruel to Presler, and has derailed his research for some time.

“In addition to his incredible abilities and creativity, he had this incredible ability to listen to a completely wrong idea in me, extract a useful piece of it, and then pass the ball back,” he says. “We had the same vision of what we wanted to achieve at work, and it pushed us to try to tell a certain story. At the time, almost no one was following that particular kind of work, and it was kind of aloof. But he trusted me, and encouraged each other to keep going when it seemed like Things are bleak.”

These lessons in perseverance feed Bresler as he and his students continue to explore questions that are inherently difficult to answer.

One area in which he has worked intermittently for more than a decade involves learning graphical models from data. He shows that models for certain types of data, such as time series data consisting of temperature readings, are often generated by domain experts who have relevant knowledge and can build a reasonable model.

But for many types of data with complex dependencies, such as social network or biological data, it is not at all clear what structure the model should take. Bresler’s work seeks to estimate a structured model of data, which can then be used for downstream applications such as making recommendations or better forecasting the weather.

He says that the fundamental question of defining good models, whether through algorithms in a complex environment or analytically, by defining a game model useful for theoretical analysis, links abstract work with engineering practice.

“In general, modeling is an art. Real life is complex, and if you write a highly complex model that tries to capture every feature of a problem, it will fail,” says Pressler. “You have to think about the problem and understand the practical side of things at some level to determine the correct features of the problem to be modeled, so that you can hope to actually solve it and gain insight into what one should do in practice.”

Outside of the lab, Pressler often finds himself solving very different types of problems. He is an avid rock climber and spends much of his spare time rock climbing all over New England.

“I really liked it. It’s a good excuse to get out and plunge into a completely different world. Although there is a problem-solving, and there are similarities on a philosophical level, it’s quite orthogonal to just sit back and do the math.”