Photo Credit: T. Broderick

August 2019

From powers of two to Bayesian machine learning

Prof. Tamara Broderick's early passion for Math along with the support of her Father and many infuential faculty guided her to Ph.D. research and ultimately to MIT as a faculty member in EECS.

J. Carota | CSB Grad Office

As a young girl growing up in Parma, Ohio, Tamara Broderick was fascinated by the powers of two. Although she didn’t have a name for it at the time, she enjoyed starting from two and recursively adding each number to itself up to 8,192 and beyond. Her love for math was recognized and appreciated by her dad, and he made every effort to find opportunities for her to participate in and nurture that passion. “My dad has always been really amazing at looking out for me. Even though he doesn’t work in math or science, he would find these great opportunities, like summer programs. He realized that math was something that I liked a lot. He appreciated that, and he made it possible for me to study it further,” Broderick explains.

When Broderick was in the eighth grade, her teacher, Ms. Moran, also took notice. She pointed Broderick and her dad to high-achieving high schools in the area. Thanks to these pivotal conversations and the life-changing opportunity provided by financial aid, Broderick was able to apply to and attend the selective Laurel School, a high school in Shaker Heights, Ohio.

Broderick recalls the teaching quality at Laurel School as being extraordinary. For instance, her physics teacher Dr. Reza Beigi was able to facilitate a connection at Case Western Reserve University so that Broderick could start pursuing astrophysics research. Broderick counts herself fortunate to have had the opportunity. “It was huge that I was able to work on research so early. I got to work with this amazing guy who was a postdoc at the time, Dragan Huterer. He was incredibly patient and engaging with me as a high schooler. Together with the summer programs, this experience made me very excited to one day conduct research in graduate school,” remembers Broderick.

English teacher Jeanne Stephens enlightened Broderick on how to effectively communicate her written research. A lot of Broderick’s work now consists of mathematical proofs. “Proving that a mathematical fact is true is very similar to a logical argument in English, and I think the training I got from Ms. Stephens was fantastic.” 

Laurel School was also one of few schools at the time to offer multivariable calculus. Her teacher Dr. Ellen Stenson taught the class of just three students, including Broderick. Broderick is especially grateful to have had the experience since it gave her the strong mathematics background necessary to major in math at Princeton University.

At Princeton, undergraduates were not permitted to major in more than one subject. Determined to not let this derail her interests, Broderick simply took all classes as though she were pursuing a triple major in math, computer science, and physics.

As an undergraduate student, she continued her exploration of astrophysics with research in the lab of Prof. Uros Seljak, where she worked closely with then-graduate student Rachel Mandelbaum. In later years she performed research with Prof. Rob Schapire, who worked in computer science, and with Prof. Bill Bialek, who worked in physics and genetics. “I was still exploring – I had no idea what I wanted to do next. Math, physics, and computer science all sounded great, but each one is a humongous area. I didn’t know which one I would end up in,” Broderick recounts.

Upon graduation from Princeton she needed time to narrow down her interests. She was grateful to be able to take that time with a prestigious Marshall Scholarship, which provides financing for Americans to study in the United Kingdom for two years. Broderick chose to study at the University of Cambridge, a choice that aligned well with her interests. At Cambridge, she obtained a master’s in math and in physics.

While at the University of Cambridge, Broderick continued to pursue research. For instance, she worked with Prof. David MacKay on applying machine learning ideas to assistive technology. She designed an interface, “Nomon,” to allow people with extreme motor impairments to type quickly, use GUIs, and draw on computers. Broderick is still passionate about Nomon today and has revived the project in her own lab.

At Cambridge, Broderick also worked with Prof. Robert Gramacy on developing machine learning tools that use “Gaussian processes,” which provide a particularly flexible way to fit patterns in data and also allow for quantification of uncertainty.

Broderick describes her time in the UK as “really affirmative. I was very lucky to go to Cambridge and be able to work with Bobby Gramacy and David MacKay. It was during my time at Cambridge that I finally realized how my seemingly disparate interests fit together in one research area called Bayesian machine learning. It has the elegant mathematics of probability theory. It is incredibly useful and can be applied to solve a wide range of real-life data analysis problems. And it has the interesting algorithmic component that I was looking for on the computer science side. I really wanted to dive deeper in this area.”

After applying to the UC Berkeley graduate program in statistics, she was accepted and started her Ph.D. research on Bayesian nonparametrics, a subset of Bayesian inference, with Prof. Michael I. Jordan.

At UC Berkeley, she worked with Prof. Jordan and Prof. Jim Pitman on open questions in Bayesian inference – including what models can be used in practice and how to make inference fast and easy to use for practitioners. She collaborated with several labs, including Prof. Yun Song’s lab, which focused on mathematical and computational biology.

When Broderick wasn’t in lab and needed to get out of her headspace, she found refuge in the graduate student co-op she joined in her first year. The chores she shared with the other house mates gave her a sense of accomplishment if she was feeling unproductive in lab, and she appreciated the social aspect. The exchange of ideas between students in a wide variety of departments represented her ideal of academia.

As she approached the end of her Ph.D. she knew she wanted to remain in academia. What she loved most was the freedom it offered and the ability to set your own research agenda. Broderick applied to several faculty positions, including one at MIT in the department of Electrical Engineering and Computer Science. 

Upon receiving an invitation to interview at MIT, she traveled to campus. “One thing that struck me when I visited MIT was how friendly everyone was. Everyone was so brilliant, but in a very open and friendly way. They were very interested in chatting about exciting ideas. It struck me as being a really nice environment,” remembers Broderick.

When offered the position as Assistant Professor in 2015, Broderick was excited to accept. “It’s just an amazing world-class institution. Being here is a huge privilege. I am around so many resources and world-class people working in interesting areas. I get to have so many amazing experiences.”

Broderick explains her lab’s objectives: “We are interested in understanding not just what we know but how well we know it. In machine learning, we try to find and use patterns in data. Bayesian inference lets us understand how certain or uncertain we are about anything we’ve learned. In my group, we try to make it fast and easy for practitioners to learn from data, to evaluate their uncertainty, and to understand how robust their inferences are to any assumptions. We want to be able to provide theoretical guarantees on the quality of the output of our algorithms.” One of their projects takes a very large data set, which might slow down typical machine learning algorithms, and compresses it to a much smaller weighted data set. Machine learning algorithms run fast on the smaller data set and, if the small data set is constructed carefully, can (provably) give almost the same answers as if they were run on the full large data set.

Other projects in the Broderick lab relate to Bayesian nonparametrics, which allows practitioners to learn more from data as they acquire more of it. For instance, we might discover more topics as we read more articles from Wikipedia or find more social groups as more people interact on Twitter or Facebook. 

After quickly setting up her lab in EECS, Broderick also continued and expanded her collaborations, which span the globe. For instance, she continues to work on Nomon, now with an MIT undergraduate student, Nicholas Bonaker, and with collaborators Dr. Emli-Mari Nel in South Africa and Prof. Keith Vertanen at Michigan Tech.

As a woman in science, Broderick feels “very grateful to have received support from wonderful mentors and peers” and wants to pay it forward. She notes, “I was lucky to be a student in the first ever instance of the Women’s Technology Program at MIT. WTP is a summer program for young women in high school. They learn about electrical engineering and computer science or mechanical engineering. Earlier this summer, I had the opportunity to talk to this year’s students about machine learning, and I got to tell them about my own great experience at WTP.” She also serves on the board of directors for the Women in Machine Learning (WiML) organization. WiML organizes an annual workshop that occurs right before the Neural Information Processing Systems (NeurIPS) conference.  The WiML workshop provides a venue for women to present their research and make connections with other women researchers before NeurIPS.

As Broderick reflects on her Ph.D., a lot of it was “driven by this need to understand. As you get closer to the frontier of human knowledge the more you realize there are giant gaps, and research is just starting to fill in those gaps. With each piece of work, we get to push that frontier a little bit further out.”  She encourages students with the same curiosity and ambition to pursue a PhD. “Being in this job, we get to explore very exciting questions. I think what is exciting and scary about research is that you really don’t know the answer going in. You have an intuition, but you don’t know the answer, and that’s the whole point.”