Thesis advisors place hoods on new Ph.D. graduates
As Associate Director for Graduate Studies in 2002, current ORIE Director David Shmoys initiated a hooding ceremony for new Ph.D. graduates to mark the completion of their studies. In this year’s graduation ceremony, four new graduates were honored in this traditional fashion. Professor Mark Lewis, the current Associate Director for Graduate Studies, introduced each student with an anecdote provided by their parents.
Wei Chen, who came to ORIE in 2009, was hooded by his advisor, Charles A. Alexander Professor of Statistical Sciences Martin Wells, a member of the Field of Operations Research who also holds a courtesy faculty appointment with the School.
Dr. Chen’s research deals with the challenges and opportunities inherent in the recent availability of massive quantities of data for analysis, the so-called “Big Data Explosion.” Methods of statistical computation that assist in understanding the structure of a set of data might not be efficient (or even feasible) when the data set is extremely large. These methods, such as Principal Component Analysis (PCA), attempt to explain data sets that measure a large number of variables (think of a spreadsheet with hundreds of columns) in terms of a much smaller number of new variables, called components, whose values can be constructed from the larger set. Such methods make it easier to visualize the data, to learn patterns, and to improve performance in fields as diverse as neurological diagnosis and financial arbitrage.
Chen has worked on a variant of PCA that seeks components constructed from as few of the original variables as possible, a variant called Sparse PCA (SPCA). He developed a computationally efficient method for SPCA that compares favorably with standard PCA on large datasets. He also developed statistical methods that can use operational data from interconnected systems of computer servers to detect when their behavior changes.
Chen received a BS in Statistics from Zhejiang University in China and an MS in Applied Math and Statistics from Johns Hopkins before coming to Cornell for his Ph.D. While at Cornell he held summer positions with Microsoft in Mountain View, CA; Nomura Securities in Tokyo; and Goldman Sachs in London. As an Associate at J.P. Morgan in New York he is “working on a project to calculate and simulate market and credit risks, and some of the problems I face are similar to the ones in my research at Cornell,” he said recently.
“ORIE provided a variety of advanced courses to broaden my knowledge,” he said, “and I’ve learned how to think independently and differently. As a foreign student, I really appreciate the education and opportunities Cornell and US have provided for me.”
Jing Xie, who holds a BS in mathematics and applied mathematics from Fudan University in China, was hooded by her Ph.D. advisor, Professor Peter Frazier.
Dr. Xie’s research considers how to choose, from a competing set of alternatives, one with the best anticipated performance, or a subset of these alternatives whose performance is anticipated to exceed a specified level. For example, the alternatives might be different ways of allocating a fleet of ambulances to bases in a city so as to meet a required percentage of on-time responses. Another example is to pre-determine, from a set of possible daily market and operational conditions, which conditions make it profitable to run a production facility, thereby furnishing the production manager a table to aid in deciding whether to run the facility on a particular day. Yet another example concerns the design of a bypass graft around a clogged artery.
In such situations, the performance of the alternatives can only be evaluated in advance by running a computer simulation many times, with input values chosen randomly each time from probability distributions that represent, for example, the occurrence of ambulance calls through the day. In practice, to choose the best alternative or set of alternatives the simulation is run the same number of times for each alternative. But running the simulation the same number of times for each alternative is usually not the most efficient way to allocate computing resources, especially if it is possible to learn, from the results of early runs, which alternatives it would be beneficial to run more or less frequently.
Xie used a variety of techniques to develop procedures for this problem, developing theoretical results about the procedures, comparing them numerically with previously developed approaches and applying them to the emergency services, manufacturing and health care applications described above. A paper based on her work was selected by the INFORMS Computing Society as the best paper at the interface of computing and operations research by a student author.
In her thesis, Xie acknowledges the “exceptional guidance, caring and patience” of Professor Frazier, as well as the faculty, her fellow students, and her parents, who were given flowers during the ceremony. Following graduation, she began work as a Risk Manager at American Express in New York City.
Zachary Rayfield, a mathematics graduate of the University of Maryland Baltimore County, was hooded by his Ph.D. advisor Huseyin Topaloglu.
Dr. Rayfield’s thesis is in an area of marketing research called customer choice modelling, which deals with the purchase reaction of customers confronting an array of products and prices in an online or physical store.
For example, a customer may use a travel aggregation web site such as Kayak or Expedia to plan a trip, first selecting a site and then choosing from among competing alternatives displayed on it. Rayfield developed a sequential procedure by which the hotel, airline or rental car firm can determine the best prices to charge for their offerings on these sites.
For the situation in which the vendor offers an assortment of products (for example, different travel packages) with different attributes, finding best prices is computationally intractable, so Rayfield developed a method for determining approximately optimal prices, including the case when prices must lie within a specified range that meets the expectations of the customer. He extended the method to determine not only the prices, but which assortment to offer.
When the vendor is a ‘brick and mortar’ establishment, whether a specialty store or a so-called Big Box store, determining which assortment of products to stock, how much of each to stock, and how to price them is a complex problem. Using a variety of mathematical techniques, Rayfield demonstrated relationships between the evaluations of individual products (which may be correlated with one another) and optimal product variety, optimal inventory levels and optimal profits. “The relationships demonstrated align with trends observed in practice,” he notes.
At the commencement ceremony, Director of Graduate Studies Professor Mark Lewis noted that in addition to his research, Rayfield is deeply involved with music as a pianist and composer. He is now in the Revenue Management and Analytics division of the Walt Disney Company at Disney World, a group that supports many lines of business including parks and resorts, merchandise studies, and media networks. He is currently working on systems that identify which combinations of stay options to offer to prospective guests and determine whether to accept or deny requests at a given time at Disney World resorts, a project that is closely related to his thesis.
Rayfield says that “the friendly, collaborative atmosphere and camaraderie among the graduate students is what I will remember most about both ORIE and Cornell as a whole. I very much enjoyed my time as a member of this community.”
Mutiara Sondjaja, known as Tia, was hooded by her advisor, Professor James Renegar. Born in Indonesia, she received her undergraduate degree in mathematics from Harvey Mudd College.
Dr. Sondjaja’s thesis presents a new algorithm for computing solutions to linear programming (LP) problems and generalizes it in significant ways.
In their simplest interpretation, LP problems model the resources consumed by engaging in any mix of a set of activities, the requirements met by engaging in that mix, and the total profit (or cost) incurred by doing so, with the objective of finding a mix that maximizes total profit (or minimizes total cost) without consuming more resources than are available or failing to meet stated requirements (such as satisfying demand for a product).
LP problems are linear in that the contribution of each activity is proportional to the level at which it is conducted and the contribution of any mix of activities is the sum of the individual contributions. LP problems are formulated in algebra and are routinely solved computationally in a huge variety of real-world applications. An LP problem can also be represented geometrically in terms of a polyhedron in high-dimensional space.
The ‘classical’ approach to computing solutions to LP problems, dating from 1948 and taught to all ORIE undergraduates, goes step by step through the geometric representation, choosing which resources to completely use up and requirements to completely meet, so that the path moves along the edges of the polyhedron. Newer methods compute paths that stay within the interior of the polyhedron, typically within a series of ellipsoids (multidimensional generalizations of ellipses).
The method proposed in Sondjaja's thesis approaches the solution from both inside and outside of the polyhedron, where the outside path moves within a series of ellipsoids containing the polyhedron, and where the inside path is guided by the outside path. The paths meet at the solution. She proves key properties of the method, including that it is competitive with previous methods.
Sondjaja has extended the method to encompass problems that may lack the linear structure of LP problems, including a class of problems known as semidefinite programming (SDP), which has been a primary focus of optimization research for a decade. Like LP problems, SDP problems have broad application in engineering, industry and finance.
Sondjaja is now a Clinical Assistant Professor in the Department of Mathematics at New York University’s Courant Institute of Mathematical Sciences. She comments that she had “a very positive experience overall” at Cornell. “I continued to find my peers and the ORIE faculty members supportive” during challenging times, and appreciates “being given the opportunity to teach a course (Optimization 2) by myself, which given my interests in teaching, was a very rewarding experience in many ways."