Philippe Rigollet

I work at the intersection of statistics, machine learning, and optimization, focusing primarily on the design and analysis of efficient statistical methods. My current research is on statistical optimal transport and the mathematical theory behind transformers.

Affiliations

Mathematics

IDSS

LIDS

Broad Institute

Academic Positions

Professor

MIT, Mathematics, 2020 -

Associate Professor

MIT, Mathematics, 2016 - 20

Assistant Professor

MIT, Mathematics, 2015 - 16

Assistant Professor

Princeton, ORFE, 2008 - 14

Postdoc

Georgia Tech, Mathematics, 2007 - 08

Education & Training

Ph.D. in Mathematics

Univ. of Paris 6 (now Sorbonne Univ.) - 2006

M. Sc. in Statistics & Actuarial Science

ISUP - 2003

B. Sc. in Applied Mathematics

Univ. of Paris 6 (now Sorbonne Univ.) - 2002

Selected Awards

Frank E. Perkins Award

2023

The Frank E. Perkins Award for Excellence in Graduate Advising is given each year to a professor from each school who has served as an excellent advisor and mentor for graduate students. The award is named in honor of Frank E. Perkins, Dean of the Graduate School from 1983-95.

Medallion lecture. Joint Statistical Meetings.

2021

Lecture on "Statistical Optimal Transport". Watch video here .

Elected IMS Fellow.

2021

For outstanding contributions to the analysis of statistical versus computational trade-offs, to the theory of aggregation, and to statistical optimal transport.

Invited lecturer. St Flour Probability Summer School.

2019

Lectures on "Statistical Optimal Transport". More information here. Lectures notes will be available Fall 23.

Best Paper Award.

2013

Berthet and Rigollet received "best paper award" at the Conference On Learning Theory (COLT) for their paper "Complexity Theoretic Lower Bounds for Sparse Principal Component Detection". In this work, they show that employing computationally efficient statistical methods in the context of sparse principal component analysis leads to an ineluctable deterioration of statistical performance, regardless of the efficient method employed. In particular, their paper draw new connections between statistical learning and computational complexity. An extended version of the paper is available here.

NSF CAREER Award.

2011

Large Scale Stochastic Optimization and Statistics..

Featured Work

Transformers and Self-Attention dynamics

ArXiv 2305.05465

In this work, we view the self-attention layers of the transformer architecture as an interacting particle system that exhibits a long-time clusterting behavior. Cluster locations are determined by the initial tokens, confirming that transformers learn context-aware representations. The system of ODE and associated PDE have a quite rich stucture and this is a topic we are actively working on.

Wasserstein gradient flows

YouTube EBA0NyY4Myc

This talk gives an overview of our recent work on applications of Wasserstein gradient flows to problems arising in statistics and machine learning. The Wasserstein geometry and its extensions (notably Wasserstein-Fisher-Rao) provide a toolbox to develop particle-based optimization algorithms over probability measures. These ideas have been implememented in several examples such as variational inference and nonparametric maximum likelihood estimation.

Biological applications

ArXiv 2306.03218

Our group explores applications of novel mathematical ideas to biological data, including genomics data in collaboration with the Eric and Wendy Schmidt Center at the Broad Institute. Our past work has focused on using optimal transport and the Gromov-Wasserstein framework to combine multiple sources of data and we are currently exploring new tools for new applications, including spatial transcriptomics.

Research Group

Aleksandr Zimin

Ph.D Student

Anya Katsevich

NSF Postdoc

Borjan Geshkovski

Postdoc

Enric Boix Adserà

Ph.D Student

George Stepaniants

Ph.D Student

Hannah Lawrence

Ph.D Student

Max Daniels

Ph.D Student

Patrik Gerber

Ph.D Student

Yajit Jain

EWSC Postdoc Fellow

Yihang "Kimi" Sun

UROP

Yuling Yan

Wiener Postdoc

Ziang Chen

Instructor in Applied Math

Openings

Interested in joining our group?

I cannot answer direct requests but you are encouraged to explore the various oppotunites at both the graduate and the postdoc levels. Make sure to check this page regularly, especially in the Fall.

Instructor

Applied Mathematics

3yr postdoc with higher salary and teaching duties

Postdoc

Fondations of Data Science Institute

I am a co-PI at FODSI, the Foundations of Data Science Institute. We are looking for postdocs starting September 2024. Please apply here and list me as one of your potential mentors.

Postdoc

Eric & Wendy Schmidt center

I am looking for postdocs interested in exploring new connections between mathematical methods and biology, esp. genomics. The new Eric & Wendy Schmidt postdocs offers a perfect opportunity for such collaborations.

Wiener Fellowship

Statistics and Data Scence Center

The Wiener Fellowship is a competitive postdoc in the Statistics and Data Science Center at MIT. Laureates are expected to collaborate with several members of the center

Ph.D student

Mathematics department

This group admits Ph.D. students exclusively through the Mathematics department at MIT. Decisions are made at the departmental level rather than at the faculty level.

Current Funding

NSF CCF-2106377

Collaborative Research: CIF: Medium: Analysis and Geometry of Neural Dynamical Systems

NSF DMS-2022448

TRIPODS: Foundations of Data Science Institute

NSF IIS-1838071

BIGDATA:F: Statistical and Computational Optimal Transport for Geometric Data Analysis

Contact

The best way to contact me is via email

View Email Address