Graduate studies: a consistent model for success

Four graduate students were awarded a departmental research presentation award by the Department of Statistics and Actuarial Science, but that's not all they have in common. They all came to Waterloo because they knew of the excellence of the Statistics programs, research, and professors. Their backgrounds vary, as do their research areas, but they have all had a great experience.

During an eight-month co-op term, Yuliang Xu's research project focused on building a statistical model for risk factors of breast cancer. Working with Laurent Briollais at the University of Toronto, she developed a statistical model to identify risk factors, and a dynamic prediction to help clinicians tell patients when they should return to the hospital for screening to lower their risk of breast cancer.

After completing her undergraduate degree in Pure Mathematics and Applied Mathematics at the South China University of Technology, Yuliang went on an international exchange. She attended Western University and took some statistic courses.

“When I was at Western, a stats PhD student told me about the University of Waterloo and all of the prestigious professors,” said Yuliang. “Also, it’s a prestigious program, so most Master’s students are expecting good job opportunities if they choose not to do a PhD afterward." Yuliang is one of those students who’s choosing to do a PhD, which she will start in September at the University of Michigan.

Maysum Panju, a PhD candidate in his fourth year, focused on tackling a problem called symbolic regression. Symbolic regression asks why we should assume that we know what the pattern is based on the input variables, and instead looks at the data to find the best possible model that will fit without making any assumptions that we know the output. It produces a rule in the form of arbitrary mathematical expression with no pre-specified structure. The availability of neural networks has given Maysum a new way to tackle this problem. Working with Ali Ghodsi, he’s making progress towards developing models that work with consistent success.

“A common application of this could be learning the natural laws of physics. If you’re given data about a physical system, you don’t necessarily need to know the different physical laws, you can uncover the laws by uncovering the data sets only,” explained Maysum. “That’s the problem I was trying to solve.”

Attending high school in Toronto, Maysum always knew that you the place to go for mathematics was the University of Waterloo. He completed his undergraduate degree and Master’s in computational math, where he first learned about machine learning. With a background in computing, his interests in developing algorithms and theoretical proofs led him to his PhD in statistics.

Entering the fourth year of her PhD, Menglu Che is working on the incomplete data problem. Working with Jerald Lawless and Peisong Han in the area of biostatistics, Menglu is interested in developing new methodologies for this type of unique data. When completing sample surveys on a large population, the first phase often consists of collecting easy-to-measure variables such as height, age, and gender. However, some variables, such as an individual's genome, can be costly to measure. This prohibits large samples, so in the second phase only a small sample is collected for that type of variable. The large data set of easy-to-measure variables can still be used to develop models to make connections to those hard-to-measure variables.

Menglu came to Canada after finishing her undergraduate degree in mathematics at Zhejiang University to complete a Master’s at the University of Alberta. It was there that she started taking statistics courses and decided to complete a PhD in statistics.

“My interest is mainly in mathematical statistics, which deals more with methodology and theory. I think Waterloo has a good selection of classes in those areas, and of course a lot of good researchers, and I’ve learned a lot from them,” noted Menglu. “I decided to come to Waterloo because it was such a celebrated university in this area of research.”

Erik Hintz, now in the third year of his PhD, is supervised by Christiane Lemieux and Marius Hofert. One of his research projects focused on computing multivariate normal variance mixtures, research directly applicable to risk management. Erik and his supervisors are numerically approximating the probability that a collection of certain random components such as stock prices, falls in between some user-specified range using specific methods and software. For example, if you wanted to model two stocks and approximate the probability that both stocks are simultaneously dropping by more than 25%, that probability can be approximated (under some model assumptions). 

After studying Mathematics and Management (BSc and MSc) at the University of Ulm, Erik completed an MMath here at Waterloo in Statistics. Great friends and supervisors with whom he enjoyed working with, made the decision to complete a PhD program here quite easy. He also enjoys doing the research he cares about and the potential for personal development.

“I have the freedom to broaden my knowledge in other areas and develop other relevant skills, such as programming, presenting research, and teaching classes. As such, I had the great opportunity to present my research at a large conference,” said Erik. “Another good experience was teaching a fourth-year course about quantitative risk management, an area closely related to my research, on my own.”