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Author: Salena Fitzgerald
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Dmitriy Kunisky joined the Department of Mathematics and Statistics on July 1 from Yale University, where he served as a postdoctoral researcher. The new assistant professor’s research explores the intersection of probability theory, mathematical statistics, computational complexity, and algorithm theory.

Tell us a little about yourself.

I was born in Moscow, Russia, and when I was five years old, my family moved to the United States. I grew up in the sunny suburbs of New Jersey and stayed nearby for my undergraduate degree in mathematics at Princeton University. Afterwards, I worked in the industry for two years, first as a freelance software engineer, and then for Google in California, and later transferring to New York. I completed my PhD in mathematics at the Courant Institute at New York University and then was a postdoc in computer science at Yale University until joining Johns Hopkins this summer.

I like to read, particularly offbeat modern fiction and hope someday soon to brush up on my Russian enough to get a Russian novel in here and there. I am also an amateur but avid musician; as I write this, sundry instruments not yet unpacked in my apartment are tempting me away.

I am interested in the relationship between probability theory (the study of randomness) and computational complexity (the study of algorithms). This relationship has become increasingly important in statistics: While early work on statistics assumed implicitly that datasets would be small enough (describing, say, two properties of each of 20 people) to allow you to calculate anything you wanted about them, modern datasets have turned out to be massive and high-dimensional. Understanding when we have the computational resources to handle these new situations reveals fascinating new mathematics.

As one example, I’ve spent a lot of my time in recent years thinking about “information-computation gaps,” a phenomenon in which a dataset contains enough information to answer a statistical question like “Do the people in our sample come from one homogeneous population or from two distinct ones?” but that information is intractably hard to access by all appearances, and no efficient algorithm can answer the same question.

What are some real-world applications of your research?

One valuable idea my research community has focused on is that of general algorithmic frameworks that are flexible enough to address many statistics or optimization problems in a unified and systematic way. My work has looked at classes of algorithms that utilize convex optimization and those that involve computing with low-degree polynomials. Reasoning with the general analytical tools we have developed for these algorithms can let us quickly understand when a statistical problem should be tractable. These general-purpose algorithms may not be the fastest, but they have often been an important first step in attacking a new computational task. In many cases, more focused research, combined with the knowledge that a given problem should be solvable, has resulted in more tailored and efficient algorithms.

However, other research in my field suggests that we should exercise extreme caution when drawing statistical conclusions from high-dimensional datasets. The reason why a question like the one I described above can be so computationally difficult to answer is that a large sample of people may have so many possible divisions into two candidate groups that, even if the sample truly comes from one uniform population, there may be a way to divide them so that they appear to come from two very different ones. That is, there are new and complex ways that we might make “false positive” findings, seeing illusory structure in large datasets. Our work helps to identify when this is a risk and to develop more sensitive statistical procedures that avoid such issues.

What drew you to this field and focus area?

As an undergraduate, I was interested in probability theory, but only in the classical sense: The classes I most enjoyed were about aspects of probability that were closely related to physics, such as Brownian motion (how heavy particles diffuse) and percolation (how water creeps through a porous medium). But when I returned to graduate school, I still wasn’t sure what I wanted to work on. There, I took a class on Mathematics of Data Science, taught by Afonso Bandeira, who would later become my PhD advisor, that had a significant impact on my research interests: it portrayed this area as one that, on the one hand, was directly grounded in important current applications, and on the other, had connections not only to probability theory but also to further reaches of mathematics such as abstract algebra and number theory. I was immediately captivated by the diverse range of tools and resources, as well as the numerous seemingly simple open problems that we discussed in class. I started working on one of them alongside Afonso, and the rest is history.

What excites you about bringing this work to Johns Hopkins?

When I visited Johns Hopkins to interview, I was struck by the interdisciplinary work that many in the engineering school told me about, and by the amount of contact between students and faculty in different departments, including the famous medical school. I had already been hoping to move in my research towards more applied work with more domain-specific collaborations (some of which I had participated in in the past and found most rewarding) rather than just studying computation in the abstract. The university and especially the engineering school seemed to have a tremendous volume of this kind of collaborative energy, and my visit left me very excited to explore such opportunities, both in the rapidly growing AMS department and elsewhere at Johns Hopkins.

What are some of your goals for this first year at JHU?

In my first semester at Johns Hopkins, I’m teaching a course on random matrix theory, one of the technical areas that intersect with most of the research problems that I work on, and I’m looking forward to meeting graduate students and learning about their interests and backgrounds. I would be delighted if some of them became interested in working on a research project with me. I’m also hoping to form collaborations with my new colleagues in the department and across the engineering school. And, of course, I intend to thoroughly investigate the crab cake options in town.

Anything else we should know? Any fun facts?

I chronically jump around different hobbies: When I was younger, I spent one summer convinced that I could beat the world record for the longest flight time of a paper airplane, and another generating fractal flames (the pictures in the old Electric Sheep screensaver) painfully slowly on my laptop. These days, I mostly play the guitar, hunt around distant grocery stores for new ingredients (a recent discovery: preserved lemons), and do my best to get a game of tennis in sometimes.