On transitions and connections with a statistician: Meet our PIMS PDF at UBC, Nabarun Deb.
By Lisa Sammoh, Communications and Events Assistant.
Transitional moments in life can be momentous and rewarding at the same time, and Nabarun Deb is a perfect example of this statement. After completing his masters degree in Statistics in India, he made the move to the “Big Apple” (New York) in 2017 to join Columbia University as a Ph.D. candidate. “In Columbia, I developed a passion for optimal transport, an ideal blend of probability theory and statistical methodology”, he says. Over the next five years, Nabarun’s journey has had moments of deep connection with peers, as well as exciting new opportunities in his academic career. One such avenue was optimal transport. For statisticians such as himself, it was a relatively new and exciting area with never ending paths to explore. In fact, this was how he ended up coming across the PIMS PDF position on optimal transport at UBC with a dedicated group of specialists in the area. Nabarun applied and got accepted for the position, and joined UBC as a postdoctoral fellow with PIMS in August 2022, and since then, says, “It has been a blast.” Now, we have connected with Nabarun to catch up on his research and well-being since coming to Canada.
Tell us about your academic journey; what field are you in and what is your current research on?
I did my undergraduate and master's degree in Statistics at the Indian Statistical Institute in Kolkata, India. To be honest, statistics came out of the blue for me as I didn’t take the course in high school. So I guess I flipped a coin and got lucky there. I then joined Columbia University as a Ph.D. candidate for the next five years. The move from rural India to the Big Apple was quite a transition. Thankfully, I had amazing friends and two of the nicest supervisors, Prof. Bodhisattva Sen and Prof. Sumit Mukherjee, to see me through the challenges.
After my Ph.D, I came across the PIMS PDF position on optimal transport. The position seemed like an ideal fit for me as I was already working in the field of optimal transport. My interest lies in applying optimal transport to classical statistical problems with an emphasis on distribution-free hypothesis testing.
Currently, I am working more on the mathematical side of things in an attempt to relate statistical applications of optimal transport to the rich theory of Markov processes. For example, consider 10 storage warehouses and 10 distribution centers. You have 10 trucks to transport goods from one warehouse to one distribution center. Depending on the distance between the two locations, I have to deduce the most efficient way of achieving this. It may not seem particularly enticing at first glance. However, over the years, the simple principle at the heart of solving this problem is finding application areas ranging from partial differential equations to artificial intelligence, and, dare I say, pretty much everything in between.
I am fortunate to be supervised by Geoffrey Schiebinger (UBC), Young-Heon Kim (UBC), and Soumik Pal (UW, Seattle), who have been patient and generous with their time. We are currently working on tracking the evolution of the Sinkhorn algorithm, arguably the most popular algorithm to compute optimal transport, which leverages the theory of Markov diffusions and parabolic partial differential equations.
Please share with us a few publications from your research.
The two papers, Multivariate Rank-based Distribution-freeNonparametric Testing using MeasureTransportation and Efficiency Lower Bounds for Distribution-FreeHotelling-Type Two-Sample Tests Based on Optimal Transport, show how optimal transport can be used to construct distribution-free tests for the multivariate two-sample equality of distributions testing problem and the multivariate independence testing problem. Simply put, optimal transport helps us define a notion of multivariate ranks which can be viewed as a direct extension of the notion of univariate ranks, despite the fact that higher dimensional Euclidean spaces are not equipped with a natural notion of order.
Rates of Estimation of Optimal Transport Maps usingPlug-in Estimators via Barycentric Projections focuses more on the machine learning aspect and we obtain rates of convergence of empirical transport maps to their population versions, given a large number of random samples. In fact, we are attempting to extend this line of work in my PIMS PDF position currently.
Are you teaching this semester? What has the experience been like?
I am teaching a small class on Integral Calculus this semester. The students are primarily from the Life Sciences. I believe that communication is a key skill to have in academia. In particular, small classes at UBC feel uniquely suited to sharpening communication skills. From them, I get to effectively instruct students from a non-mathematical background, since the course is designed to be interactive for students with consistent teamwork, class discussions, and direct one-on-one discussions. It has been an enriching experience thus far.
What do research and life balance mean to you? What does a typical Sunday look like?
I do enjoy writing as a way to decompress after work. You can also never go wrong with rewatching the occasional F.R.I.E.N.D.S. or Sherlock rerun. More so now, I love watching historical movies and listening to bands like Snow Patrol. I am also a big fan of watching (and hopefully playing someday) tennis. Whenever the opportunity presents itself, I enjoy a good hike too.
What are you looking forward to about your time in Vancouver and your position at UBC?
I am looking forward to setting up connections with experts on optimal transport here at UBC. I also want to enhance my teaching experiences given the unique opportunity to teach smaller but well-designed classes. So far, I have found Vancouver to be a stunningly beautiful city. I love seeing all the parks and the botanical gardens spread all over the Lower Mainland area. I also love seeing the cultural diversity. You get to meet someone interesting every time you step outside your door.
Nabarun will be speaking at the PIMS Emergent Research Seminar Series, on February 1, 2023, at 9:30 AM Pacific. Details on his talk, Optimal transport in statistics and Pitman efficient multivariate distribution-free testing, can be found here.
