There was a time when, as a young assistant professor, Philippe Rigollet would finish one project and cast about for the next one. Then he arrived at MIT.
“After two months here I knew this was never going to happen to me again,” he said. It’s often said that the pace and challenge of studying at MIT is like drinking from a firehose, but in Philippe’s telling, the same is true of doing research here. In just the last three years, Philippe, who came to LIDS in 2015, has begun to explore statistical techniques for: analyzing microscopy images, working out the trajectory of how cells grow, and for averaging geometric objects. This isn’t just dabbling, either. Each project contains underlying statistical questions that hold deep interest for Philippe, and that he is trying to tease apart.
Take the Nobel-Prize-winning microscopy technique called cryo-electron microscopy (cryo-EM), for instance. The imaging method allows scientists to study biological molecules such as viruses and proteins, and even to see how they move and change as they do their jobs. The key is that samples are frozen rapidly in a random orientation and a picture is taken. Then, mathematical techniques combine two-dimensional images shot from many different directions to compile a more complete 3D picture of the molecule. This, though, leads to a problem that is “inherently noisy,” Philippe explained. “How many pictures do you need to take of a molecule before you can learn its structure?”
Current methods of mathematical analysis rely on several assumptions about molecular behavior in order to answer this question. However, in the next phase of their research, Philippe and his colleagues would like to test these assumptions, using the theoretical methods they have developed, on data from real cryo-electron microscopy — something that might become possible once cryo-EM instruments at the new MIT.nano facility are up and running this Fall.
Philippe, who is originally from France and completed his graduate training there, started his career at Princeton, in the department of Operations Research and Financial Engineering. It turned out not to be a great fit for a statistician interested in computer science. Coming to MIT, he felt, he had nothing to lose. “I thought, even if I come for only a few years, MIT is the place where I can get what I need to get things done,” he said.
When he joined LIDS, he was one of the early hires in the effort to grow the new Statistics and Data Science Center (SDSC), which is part of the Institute for Data, Systems and Society (IDSS). SDSC consolidates cutting-edge statistics and data science research at MIT, serving as a focal point for a statistics community found across many different departments and labs. “LIDS’ historical strength in applied probability is naturally connected to statistics,” Philippe said. “We use the same tools and speak the same language and it’s only natural that LIDS has now several PIs working in statistics and data science.”
From his compact, sunny office in the mathematics department, overlooking a busy stretch of Memorial Drive, Philippe also works on what’s called high-dimensional statistics. In high-dimensional data, each data point represents many different values – think of a single patient information snapshot that contains a patient’s weight, blood pressure, temperature and so on, or a single sample that contains thousands of expression levels of different genes. In this field, the problems he studies lie right at the intersection of statistics and computer science: “One of the main questions I'm interested in is optimality: if you want to achieve a certain precision [of calculation], how much data do you need, and how well can you do with methods that are constrained to be computationally efficient compared to another method?”
Other theoretical statistics problems that have caught Philippe’s attention include questions in optimal transport, for working out the trajectory of how cells grow; and in geometric data analysis, to average geometric objects, a useful way to make computer graphics smoother and more realistic.
For the former, he works with Broad Institute computational biologist Professor Aviv Regev to understand why a cell might become, say, a liver cell as opposed to a kidney cell, and how different cell types interact with the other cells around them to become what they do. Is it possible to couple these points in space and time? How can their unique trajectory from one state to another be worked out? Because scientists can’t observe populations of cells developing in real-time, the next best thing is to use statistical methods estimate how that development happens.
In the latter, Philippe works with MIT Computer Science and Artificial Intelligence Lab (CSAIL) Assistant Professor Justin Solomon on manipulating geometric objects. Here, again, each data point or unit is a population with many values – in this case, a shape or a scene. “We want to understand what the average of populations is for example,” Philippe explained. For instance, you can interpolate between shapes to smooth out 3D graphics, or impute color palettes to scenes — taking a Boston winter scene and using those colors on a scene of a Jamaican beach, for example. This is especially useful in teaching computers to recognize images with deep learning, as information about the overall geometric structure of an image might be lost when the image is fed into a deep neural network.
In all of these problems, Philippe said, “there’s really deep and interesting mathematical theory that allows me to understand what is going on at a deeper level and have an impact on methods.”
So where and how does he find these interesting mathematical problems, and what catches his attention? Some ideas come from attending talks or talking to colleagues and catching up on their work. But it’s really serendipity, Philippe said. “It’s like asking, ‘How do you choose a painting that you like?’ I don’t choose a painting that I like. I walk into a museum and see a painting that I like. And I cannot explain to you necessarily why I prefer that painting. In a way, it's a little bit like this. I'm a window-shopper, and MIT is a great place for that,” he said. “I think I'm getting more and more curious as I get a bigger and bigger picture.”