Hoods symbolize membership in the doctoral ranks
In a ritual signifying entrance into the community of scholars, ORIE thesis advisors placed hoods on their newly graduated Ph.D. students at a recognition ceremony for Ph.D. and Master of Engineering degree recipients and candidates on the weekend of the 2013 Cornell commencement.
The hood, a distinctive component of academic garb, is a medieval relic descended from cowls worn by monks, probably to ward off drafts in monasteries. Rolf Waeber, Yi Shen, Dmitriy Drusvyatskiy, Mathew W. McLean, Takashi Owada, Kunlaya Soiaporn, Bradford S. Westgate, and Shanshan Zhang received their hoods at the ceremony.
Professor James Renegar described the research, background, and next career steps of each newly hooded individual. The scope of their research, discussed below, ranges from methods for analyzing ambulance travel times, optimizing drug development, and interpreting brain images to explorations of the properties of fundamental models in optimization and applied probability theory.
Bradford S. Westgate
When a medical emergency arises and an ambulance must be sent, determining which of the ambulances at different locations can get there fastest requires a method of estimating travel times between any pair of points in a city. A computerized system that assists this and other decisions needs to go beyond estimates of average travel times to take into account the whole probability distribution of travel times, in order to assure that contractual obligations - such as a required percentage of arrivals within 8 minutes - are met.
GPS units on ambulances in cities like Toronto, Canada, record time and position throughout their routes, thereby providing data on potential route segments in the city. However these measurements are variable and may include speed and location (right) inaccuracies. Careful statistical analysis is needed in order to convert the historical data collected in this way to information that is useful in operations and planning.
For his thesis, "Travel Time Distribution Estimation for Ambulances Using GPS Data," Dr. Westgate developed two methods that convert GPS data into useful travel times. One builds on estimates of travel time from the detailed path taken by each vehicle, the travel time on each road segment it traverses, and possible errors in the GPS data. Another works with entire trips, taking into account the time of day and the different types of roads that were traveled. In both methods, the computer learns how to improve estimates using the techniques of Bayesian statistics. The methods have broad applicability.
Assistant Professor Dawn Woodard advised Westgate’s research and placed his hood at the ceremony.
Westgate grew up in Nashua, NH, where he was homeschooled through high school. He was a member of one of the earliest classes to graduate from the new Franklin W. Olin College of Engineering, which opened in 2002. He will be a visiting assistant professor at Mt. Holyoke College, teaching probability and statistics.
Dr. Waeber analyzed and extended an optimization method applicable to a vast array of important problems, such as designing drug development trials to quickly obtain the optimal dosage or designing simulations of service, industrial and other systems to obtain optimal control values. Such problems have the characteristic that repeated experiments (with different random groups of patients, customers, or parts) yield results differing in significant ways, i.e. they are probabilistic in nature.
Waeber‘s research focused on a particular method that is a probabilistic version of bisection search, a standard but not necessarily efficient approach for finding the point where a function evaluates to zero (the root). This approach proceeds by bracketing the root with inputs that yield positive and negative function values and then choosing successively smaller intervals that contain the root.
In the stochastic case there is some probability that an observed function value (dots at right) comes up positive but the input is actually on the ‘negative’ side of the crossing point (of the blue and dashed lines) or vice-versa. To overcome this, bisection search must be modified - which it was, nearly 50 years ago, but without theoretical guarantees. Waeber provided theoretical underpinnings for probabilistic bisection search, used a Bayesian approach to extend it to be useful for a broad class of applications, and showed why it is an efficient way to proceed.
Waeber’s thesis was advised by Professor Shane Henderson and Assistant Professor Peter Frazier, who placed his hood.
Waeber grew up in the Swiss Alps and completed Bachelor’s and Master degrees in Mathematics at the Federal Institute of Technology in Zurich. His doctoral work has applications in mathematical finance: after completing his doctoral thesis, “Probabilistic Bisection Search for Stochastic Root-Finding” in January 2013, he joined a boutique high-frequency trading firm in New York City as a quantitative researcher.
In June, Waeber and Xiaofei (Sophia) Liu were married. Liu obtained her Ph.D. in ORIE in 2011 and works for Credit Suisse in New York City.
Mathew W. McLean
As an applied statistician, Dr. McLean deals with huge data sets recorded from phenomena that evolve over time and or through space. Conventionally, for example in ordinary regression analysis, the relationship between input (independent) and output (dependent) observations is modeled by assuming that the relationship has a particular form, such as linear, and then computing the most likely values of the parameters that determine the relationship.
But when the input observations are images of a tract in the brain and the output observation is the score on a cognitive test, or the input observations are the bids received in the early days of Ebay auctions and the output observation is the closing price (both examples on which McLean has worked), the relationship cannot be readily characterized by such conventional methods despite the availability of data collected at very frequent intervals in space or over time.
So McLean has developed a model that can be fit to these huge data sets but relaxes the restrictive assumptions on the relationship between the input and output made by previous approaches, while remaining easy to interpret.
He has used this approach to enable predictions (at right) from brain images that subjects do or do not have a neurological disorder such as multiple sclerosis (MS), and predictions of the closing prices in Ebay auctions using only bids received in the early days of the auctions.
For his thesis, "Functional Generalized Additive Models," McLean was advised by statisticians ORIE Professor David Ruppert and Biological Statistics and Computational Biology Associate Professor Giles Hooker. At the ceremony he was hooded by ORIE Associate Professor Huseyin Topaloglu.
McLean grew up in Winnipeg, Canada, where he obtained his bachelor’s degree in statistics from the University of Manitoba. He is now a postdoctoral researcher at Texas A&M University.
Dr. Soiaporn’s work in applied statistics covers problems at a remarkably wide range of scales. One problem she has worked on is at the microscopic level, dealing with multiple sclerosis (MS), while another is astronomical in nature.
For her thesis, "Modeling Multiple Correlated Functional Outcomes with Spatially Heterogeneous Shape Characteristics," Soiaporn analyzed data, derived from the same source as McLean's MS work, that represented three different series of measurements along a tract in the brain. She developed a mathematical explanation of the relationship between the three measurements, identified where the abnormalities are, and used the observed difference to classify whether a specific patient has MS.
Soiaporn’s astronomical work, in collaboration with her advisor Professor David Ruppert and three Cornell astronomers, dealt with ultra-high energy cosmic rays, which are very rare particles that hit the Earth’s atmosphere with energies over ten million times those achievable by human-made particle accelerators. The team’s statistical model can be used to study various properties of particles detected on earth – where they came from, how they got here, and what their components are. The approach has associated specific instances in which ultra-high energy cosmic rays have been detected at locations (green dots at right) on earth with nearby galaxies (other dots) that are known to emit especially high levels of radiation from their centers.
Soaiporn was born and raised in Bangkok Thailand. She earned a Bachelor’s degree from ORIE before continuing on for her Ph.D. work. In the absence of Professor Ruppert, Associate Professor Peter Frazier placed her hood during the ceremony.
The driving theory and algorithmic techniques for optimization – finding solution values that maximize or minimize a mathematical relationship, or objective function - is illuminated by geometry. Dr. Drusvyatskiy has developed new geometric insights that significantly advance the theory of optimization algorithms as well as the theory of how optimal solution values change when the inputs to the relationships change slightly, known as sensitivity analysis.
Intuitively, for a relationship modeled with a smooth curve, the slope of the curve points the way to the maximum or minimum. Even if the model is not smooth, “various notions of 'slope' pervade optimization” and related areas of mathematics, according to Drusvyatskiiy.
In one part of his thesis, "Slope and Geometry in Variational Mathematics," Drusvyatskiy used notions of slope to shed new light on the convergence of a computational method, due to John von Neumann in 1933 and known as the “alternating projection method,” to find a point in the intersection of two sets such as A and B at right (a form to which many kinds of optimization problems can be converted). Von Neumann’s method has been used to solve applied problems in a number of areas, including information theory, control design, image processing, and the design of the Hubble telescope. Drusvyatskiy has found mathematical conditions under which the alternating projection method converges rapidly.
In another application of his approach, he analyzed the geometry of a class of algorithms, known as “active set” algorithms, for solving nonlinear optimization problems. He showed that these algorithms can work well if the relationships involved have a certain readily visualized geometric structure, which turns out to be the case, for example, in a currently “hot” class of problems called eigenvalue optimization.
Drusvyatskiy was born in Minsk, Belarus, and immigrated to the US with his family when he was eleven years old. He has a BS in mathematics from Polytechnic Institute of New York University. He is currently at Argonne National Laboratory, and will move to the University of Waterloo as a postdoctoral researcher for a year before joining the department of mathematics at the University of Washington in Seattle WA as a tenure-track assistant professor. At the ceremony, Drusvyatskiy was hooded by his advisor, Professor Adrian Lewis.
Widely used methods to compute solutions to optimization problems typically rely on the smoothness (differentiability) of the underlying relationships in order to work properly. Real world problems that don’t have the required smoothness often have a high degree of structure nonetheless, giving hope that they can be successfully solved using these computational algorithms. In her thesis, "Theory and Algorithms for Structured Non-smooth Optimization," Dr. Zhang considered a class of structured problems that have favorable properties with respect to computational methods.
For example, one well-established algorithm, due to Broyden, Fletcher, Goldfarb and Shanno, assumes that problems to which it is applied have smooth relationships. However at least one form of this algorithm typically succeeds even in the absence of smoothness. In an effort to understand this success, Dr. Zhang explored specific good and bad (right) examples, both with the computer and theoretically. She also explored the theoretical properties of a broad class of nonsmooth relationships for which it is relatively easy to determine the sensitivity of values of optimal solutions to small changes in the input data.
Zhang was advised by Professor Adrian Lewis, who placed her hood.
Zhang was born and raised in Jiangxi, China, and earned her bachelor’s degree in mathematics from Peking University in China. She has joined Oracle Corporation in Redwood City, CA.
Dr. Shen’s thesis research pertains to random processes, which are widely used to model various phenomena in the real world, such as the response time of a web site over time or the annual amount of rainfall at a location. On the one hand, Shen considers random processes that are stationary, i.e. those whose probabilistic properties do not change over time. On the other hand, he considers certain properties - called “locations” - of a random process, such as times at which maximum values occur, times at which values exceed a given threshold, or times when the largest jump occurs. For each random process, these locations themselves have probability distributions.
Under the guidance of Professor Gennady Samorodnitsky, Shen found an important relationship between a certain class of locations, which he calls “intrinsic location functionals,” and the underlying random process that defines them. He found a particular set of properties that this class of locations possesses if and only if the underlying random process is stationary. In this way, his thesis, "Stationarity and Random Locations," establishes a new characterization of stationarity, a characterization in terms of locations.
Shen's characterization can be applied in different ways, such as developing tests to determine whether a process is stationary; understanding queuing (waiting) systems with deadlines; and advancing a field called stochastic algebraic topology.
Shen was born and raised in Beijing, China, and has undergraduate degrees in mathematics and physics from Tsinghua University there. He obtained a degree in quantitative economics and finance from École Polytechnique near Paris, France. He will join the Department of Statistics and Actuarial Science at the University of Waterloo, Canada, as an Assistant Professor. In Professor Samorodnitsky’s absence, he was hooded by Professor Adrian Lewis.
Dr. Owada’s thesis concerns the modeling of heavy tails, those outlier events called “black swans” by essayist and statistician Nassim Nicholas Taleb (though Taleb might reject the notion that such events can be modeled). Black swans are events that have been observed to occur with higher frequency than can be modeled with the Normal or Gaussian curve that is so prevalent in probability and statistics.
A related phenomenon called long-term memory, is found in data from economics, finance, natural disasters and data network analysis but unaccounted for in elementary models. Data that evolves over time is said to have long term memory if it has characteristics that persist for numerous time periods, a phenomenon that violates a standard assumption, called independence, that is relied upon in elementary models.
Owada has advanced the fundamental theory that depicts the long term behavior of heavy tailed, long memory random (stochastic) processes. He has established new theorems that describe what happens in the long run to important measurements associated with these processes, including the maximum value the process reaches over longer and longer time intervals. He showed that the maximum value has a limiting behavior that heretofore had been unsuspected for heavy-tailed, long-memory processes. His thesis is titled "Ergodic Approach to Investigate Memory properties of Heavy Tailed Stationary Infinitely Divisible Processes."
Professor Adrian Lewis placed Owada’s hood in the absence of his advisor, Gennady Samorodnitsky.
Owada was born in Toyama, Japan. He has a bachelor’s degree in economics and a Master’s degree in statistics from Tokyo University. Prior to his Ph.D. studies, he worked at the Bank of Japan as an economist. He will be a postdoctoral researcher in the department of electrical engineering at the Technion Israel Institute of Technology in Haifa, Israel.