Math Researcher Tries to Crack Statistical 'Curse'
Cowen, an assistant professor of mathematical sciences at Johns Hopkins University, knows little about statistics; her expertise is in other areas of math. But some researchers believe this handicap may help Cowen succeed where others have failed in their efforts to crack a complex problem called "the Curse of Dimensionality."
The curse rears its head when a statistician is working with data in a sufficiently high dimensional space that it becomes impossible to make reliable predictions from the data.
But Cowen, using her expertise in combinatorics--the mathematics of finite objects and combinations of objects--believes she can sometimes sneak around the curse and pull useful information from problems that usually stump the statisticians.
"My goal is to break the Curse of Dimensionality," Cowen said. "I think combinatorics is going to help deal with this curse. We're going to come up with a very powerful set of tools that, in many practical instances, can get completely around it."
If Cowen's quest is successful, it may lead to breakthroughs in areas such as medical image processing and computer network routing.
Her novel approach received strong encouragement and a financial boost recently when the Office of Naval Research picked Cowen to receive one of its prestigious Young Investigator Program awards. The Hopkins faculty member was one of only 34 recipients this year, chosen from a nationwide field of 416 applicants. The three-year grant will provide $90,000 annually, primarily for graduate students to assist Cowen in her research.
The award was also another feather in the cap for the Mathematical Sciences Department in Hopkins' Whiting School of Engineering. Cowen was the department's second consecutive Young Investigator award winner. Last year, Carey Priebe, an assistant professor whose office is right next to Cowen's, won the honor. It is given to promising faculty members who have received their graduate degrees within the previous five years.
More than mere coincidence led Maryland Hall neighbors Cowen and Priebe to earn the same national awards, even though they come from completely different fields of mathematics.
Priebe, a statistician, had talked to Cowen about data sets that are notoriously difficult to analyze because of problems such as the Curse of Dimensionality. These obstacles were presented in a form that was new to Cowen but seemed to have promising analogies in discrete mathematics, the area in which she works.
"The mathematical world is really divided in two," she explained. "There's continuous math and discrete math. Continuous math is the study of things that change with time. So, nearly all math that's involved in physics, calculus and statistics is continuous math. Anything that involves measuring the physical universe is usually continuous math.
"However, the mathematics that deals with a computer is discrete math. Discrete math is the study of particular objects, a finite set of objects."
At many schools, faculty members from these two fields are based in different departments, even different buildings. But the math department in Hopkins' engineering school has professors from both disciplines, allowing for unusual, fruitful collaborations, like the one between Priebe and Cowen.
"The people in her field don't usually address the problems we're talking about," Priebe said. "They're not statisticians. But with her sitting in the office next to me and hearing the kind of things I was doing, for some reason it clicked between us that some things that she knew about might apply.
"Maybe it's novel because the people who know the stuff that she knows don't normally sit next to the people who try to solve the problems that I'm trying to solve. That may be one reason we can do things that haven't been done."
The approach that Cowen will use draws from graph theory and randomized algorithms. The weighted graph of pairwise distances between samples is distorted to a simpler structure in a lower- dimensional space where, nonetheless, the original distances are approximately preserved. The use of randomness allows the approximation to be constructed quickly.
Cowen, 28, joined the Hopkins faculty in 1994, a year after earning her doctorate in mathematics at Massachusetts Institute of Technology. She completed her undergraduate studies at Yale, which she entered at 16.
Despite her academic achievements, Cowen did not learn to drive until she was 25. With a tinge of embarrassment, she admits that she failed her driving test in two states before finally obtaining a license. Though she is a whiz at the geometry of graphs, Cowen had trouble with parallel parking.
"That was the hardest thing I've ever had to do in my life," she says with a laugh. "Learning to drive."
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