Nicolás García Trillos, Assistant Professor has been awarded a CAREER award

Nicolás García Trillos, Assistant Professor in the Department of Statistics at UW-Madison, has been awarded a CAREER award–the most prestigious early-career award given by the National Science Foundation (NSF). The award will be used to investigate mathematical foundations on how to enforce robustness of machine learning models.

The past few years have witnessed an expansion of artificial intelligence and machine learning in several domains of applications at lightning speed. Algorithms —in computers, in watches, in homes— routinely make use of collected data to provide recommendations, make predictions, or make decisions on our behalf. Algorithms these days write poetry, compose plays, and even create art pieces. In view of this unprecedented technological development, it is natural to ask a variety of fundamental and pragmatic questions: how can we guarantee that as these algorithms enter into more domains of our lives they will be sensitive to privacy concerns, they will make fair decisions, and be reliable and robust to data corruption? Are we ready to certify when a given algorithm complies with specific requirements and behaves in the way it is intended to? As these fundamental questions become more pressing, new paradigms to judge the success of data analysis methodologies have emerged, displacing high predictive power as the sole criterion for training models and giving more relevance to a more nuanced learning that can factor in reliability, privacy, and fairness criteria.

At a high level, Nicolás’ research seeks to explore foundational questions, both theoretical and algorithmic, in line with this expansion of paradigms. His research, however, will take a geometric and analytic perspective, something that according to him is natural, yet not a widespread viewpoint on the field.

“If decision boundaries associated with classification rules are that, boundaries of sets, then it makes sense to study them geometrically: how large are they, how curved are they, how are they affected by the presence of an adversary, and how can an adversary, thinking geometrically, take advantage of the geometric properties of a given decision boundary and relocate data points conveniently.”

In his proposed research, Nicolás aims to develop and utilize a wealth of connections between the task of training models robustly and topics in the calculus of variations and geometric measure theory, inverse problems, PDEs and control theory, optimal transportation, game theory, and other subtopics of mathematical analysis and geometry. He hopes to provide in this way a multidisciplinary and unique perspective on the topic of adversarial robustness.

Multidisciplinarity, however, is not something new for Nicolás. His PhD thesis work, for example, explores a variety of connections between graph-based machine learning algorithms and a series of geometric and analytical problems in continuum domains and manifolds. He is also used to interacting with and belonging to a variety of departments from different disciplines. Indeed, before joining the statistics department at UW-Madison, Nicolás was a Prager Assistant Professor at Brown University (a postdoctoral position in the Division of Applied Mathematics) and before that he got his Ph.D in mathematical sciences at Carnegie Mellon University. Nicolás received a Bachelor’s degree in mathematics from Universidad de Los Andes in Bogotá, Colombia.

“As a researcher, I think it is a good idea to be exposed to concepts and questions that are not immediate to you. This distance from your comfort zone keeps your motivation and inspiration high and your creativity active.”

The NSF CAREER award will also help Nicolás build a robust network of collaborations between his PhD students and other early career researchers at the regional and worldwide levels through various workshops and mentorships.

“It is definitely exciting to have the opportunity to push forward your research and at the same time be able to share it with your students, your colleagues, and other researchers, especially those at the early stages of their careers, at the regional level and beyond. ”