Sophie Dabo develops statistical approaches for infinite dimensional spaces

Biology, weather, chemistry, economics: all these disciplines now use functional data analysis. Just 20 years ago, no one could have predicted the growth of this statistical approach, which involves studying parameters that vary in time and/or space and concerns mathematical functions defined in spaces of very large or even infinite dimensions. Mathematician Sophie Dabo contributed to the development of this method in France. A university professor and member of the Modal project team at the University of Lille Inria Centre (joint with the University of Lille’s Paul Painlevé laboratory), she started to explore this field in the early 2000s.

Her story begins in Senegal: “I loved every subject at school”, she recalls. “But when the time came to specialise, just before my baccalaureate, I chose science over literature. I loved problem solving, that’s all I did! After my baccalaureate, it seemed natural for me to go on to study mathematics”, she explains. After studying at the Gaston Berger University in Saint Louis for two years, she continued her studies in France at Paris-V University.

Having just arrived from Africa, the young student was worried that her level of knowledge would be insufficient, but in fact, she had already learned the equivalent of an undergraduate degree! “I realised that I had received excellent training in Senegal”, she says. “In IT, on the other hand, we had only had one device for every ten students. We wrote out our algorithms on paper. So it was in France that I learned to type fast and program!” Because she was so far ahead, her teachers encouraged her to take additional modules. That was when she developed a liking for statistics.  In 1999, after completing a dual Master's degree and a Postgraduate Diploma (DEA), she decided to start a thesis on mathematical statistics for very high-dimensional data.

Too abstract a subject?

Within a still-reticent community, which considered the approach too abstract, only a few researchers were working on the subject, at universities such as at Toulouse 3, Paris 6 and MacGill in Montreal. At the time, there were only a few applications, which concerned meteorological parameters such as temperature or pressure profiles.

The traditional method for studying curves was to discretize[AC1]  them, i.e. extract points at regular intervals, but this means the information between these points is lost. Functional data analysis reconstructs this information by identifying the laws that describe the variation of the curve. “The difficulty lies in the fact that the variables studied lie within mathematical spaces of often infinite dimensions”, explains Sophie Dabo. Her PhD was theoretical, meaning she only worked with synthetic data: “In the end, I was frustrated at not being able to use real data”.

In 2002, after completing her PhD, she began to look for her first job, but her speciality was still often perceived as too theoretical, at best, and at worst useless or unrealistic. At the time, mathematician Anne-Françoise Yao was also working on the subject: “these criticisms were understandable”, she says. “We didn't know where this method would take us either, as its applications were not obvious, but we liked the idea of doing something other than traditional statistics!”

A wide range of applications

When she joined the University of Lille, Sophie Dabo’s work involved several areas of study: economics - the primary discipline of her new laboratory - but also the environment and ecology. Her curiosity drove her to broaden her field of applications through new collaborations. “We had a number of issues in common, and we thought long and hard together about how we could move forward in this area”, recalls Anne-Françoise Yao. The two researchers worked on spatial applications of functional data using geochemical data, which involved processing images or geographical regions: more complex than curves! Their joint work led to several publications.

New topics soon began to emerge: “another researcher at the university was studying the impact of consultation times and geographical factors on recovery from certain cancers”, explains Sophie Dabo. This was where the spatial application of functional data analysis really came into its own: what are the risk, recurrence and survival factors in different geographical areas? “It's difficult to establish spatial dependencies”, says the statistician. She analysed the environments in which patients lived, highlighting the risks associated with the proximity of certain industries, or the remoteness of hospitals. This work led to her involvement in the creation of Oncolille, an Institute for Interdisciplinary Cancer Research, where she currently heads the mathematics team.

Since then, health has been a central focus of her research. “Sophie offered to help us in 2017 when I was presenting my team's work at a conference”, recalls Dominique Collard, a physicist and researcher at the CNRS. “We had developed a microsystem for identifying cancer cells by measuring their electrical and mechanical characteristics”. Sophie Dabo suggested using functional data analysis.

Before long, these positive results led to the creation of a start-up with a view to marketing a diagnostic tool.

A direct impact on healthcare

In 2021, Sophie Dabo launched the PATH exploratory project, run jointly by the Modal project team and Lille University Hospital. It aims to model patient pathways, which are composed of a wide range of data including digital values, images and reports, some of which are on paper. “Thanks to PATH, we were able to join the EN HOPE SMART4CBT consortium, with a view to modelling the pathways of children and teenagers with brain tumours", says the researcher. The project also led to the development of a new technological component for QuantiHealth, a start-up that developed an app offering day-to-day support for diabetics, and provided a basis for Henddu, a start-up specialised in air quality analysis.

Functional data analysis has really taken off since its shaky beginnings, helped by the increased computing capacity of today’s devices, but also by “visionary scientists who saw its potential”, says Sophie Dabo. “The field has come a long way”, adds Anne-Françoise Yao. “The applications have raised new questions, to which we now need to find theoretical answers”. The list of subjects to explore is far from being exhausted!