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Summer Graduate School

Mathematics of Machine Learning (INdAM and Courant Institute) July 25, 2022 - August 05, 2022
Parent Program: --
Location: Courant Institute, New York
Organizers Sebastien Bubeck (Microsoft Research)
Teaching Assistants(s)

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Speaker(s)

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Description
Image
Popular visualization of the MNIST dataset

This school is offered in partnership with Istituto Nazionale di Alta Matematica Francesco Severi (INdAM) and the Courant Institute of Mathematical Sciences.

The schedule for the school can be found HERE.

MSRI-supported students will participate from the Courant Institute.

Learning theory is a rich field at the intersection of statistics, probability, computer science, and optimization. Over the last decades the statistical learning approach has been successfully applied to many problems of great interest, such as bioinformatics, computer vision, speech processing, robotics, and information retrieval. These impressive successes relied crucially on the mathematical foundation of statistical learning.

Recently, deep neural networks have demonstrated stunning empirical results across many applications like vision, natural language processing, and reinforcement learning. The field is now booming with new mathematical problems, and in particular, the challenge of providing theoretical foundations for deep learning techniques is still largely open. On the other hand, learning theory already has a rich history, with many beautiful connections to various areas of mathematics (e.g., probability theory, high dimensional geometry, game theory). The purpose of the summer school is to introduce graduate students (and advanced undergraduates) to these foundational results, as well as to expose them to the new and exciting modern challenges that arise in deep learning and reinforcement learning.


To get the most out of the mini-courses in the school, students are encouraged to attend all the lectures and minimize distractions. Please try to avoid the use of laptops, smartphones, tablets, etc. except for note-taking (because the material is highly mathematical, students will probably find it easier to use a pen and notebook).

Suggested Prerequisites:

  • Linear Algebra
    (e.g. https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/).
  • Probability
    (e.g. https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/).
  • Multivariable calculus
    (e.g. https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/).
  • Real Analysis
    (e.g. https://ocw.mit.edu/courses/mathematics/18-100c-real-analysis-fall-2012/).

For eligibility and how to apply, see the Summer Graduate Schools homepage

Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI.

Support for this school is provided by Scuola Matematica Interuniversitaria (SMI) and MSRI.

Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Learning and adaptive systems

  • Computational learning theory

  • Decision theory

  • Probabilistic games

  • stochastic processes

  • Neural nets

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Schedule, Notes/Handouts & Videos
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Jul 25, 2022
Monday
09:00 AM - 10:00 AM
  Lecture: Convex Optimization
Nicolas Flammarion (École Polytechnique Fédérale de Lausanne (EPFL))
10:15 AM - 11:15 AM
  Lecture: Online Learning
Nicolo Cesa-Bianchi (Universita degli Studi di Milano)
11:30 AM - 12:30 PM
  Lecture: Statistical Learning Theory
Robert Schapire (Microsoft Research)
Jul 26, 2022
Tuesday
09:00 AM - 10:00 AM
  Lecture: Convex Optimization
Nicolas Flammarion (École Polytechnique Fédérale de Lausanne (EPFL))
10:15 AM - 11:15 AM
  Lecture: Online Learning
Nicolo Cesa-Bianchi (Universita degli Studi di Milano)
11:30 AM - 12:30 PM
  Lecture: Statistical Learning Theory
Robert Schapire (Microsoft Research)
Jul 27, 2022
Wednesday
09:00 AM - 10:00 AM
  Lecture: Convex Optimization
Nicolas Flammarion (École Polytechnique Fédérale de Lausanne (EPFL))
10:15 AM - 11:15 AM
  Lecture: Online Learning
Nicolo Cesa-Bianchi (Universita degli Studi di Milano)
11:30 AM - 12:30 PM
  Lecture: Online Learning
Nicolo Cesa-Bianchi (Universita degli Studi di Milano)
Jul 28, 2022
Thursday
09:00 AM - 10:00 AM
  Lecture: Convex Optimization
Nicolas Flammarion (École Polytechnique Fédérale de Lausanne (EPFL))
10:15 AM - 11:15 AM
  Lecture: Convex Optimization
Nicolas Flammarion (École Polytechnique Fédérale de Lausanne (EPFL))
11:30 AM - 12:30 PM
  Lecture: Statistical Learning Theory
Robert Schapire (Microsoft Research)
Jul 29, 2022
Friday
09:00 AM - 10:00 AM
  Lecture: Online Learning
Nicolo Cesa-Bianchi (Universita degli Studi di Milano)
10:15 AM - 11:15 AM
  Lecture: Deep Learning Theory
Joan Bruna (New York University, Courant Institute)
11:30 AM - 12:30 PM
  Lecture: Deep Learning Theory
Joan Bruna (New York University, Courant Institute)
Aug 01, 2022
Monday
09:00 AM - 10:00 AM
  Lecture: Statistical Learning Theory
Robert Schapire (Microsoft Research)
10:15 AM - 11:15 AM
  Lecture: Deep Learning Theory
Joan Bruna (New York University, Courant Institute)
11:30 AM - 12:30 PM
  Lecture: Reinforcement Learning
Mengdi Wang (Princeton University)
Aug 02, 2022
Tuesday
09:00 AM - 10:00 AM
  Lecture: Deep Learning Theory
Joan Bruna (New York University, Courant Institute)
10:15 AM - 11:15 AM
  Lecture: Deep Learning Theory
Joan Bruna (New York University, Courant Institute)
11:30 AM - 12:30 PM
  Lecture: Reinforcement Learning
Mengdi Wang (Princeton University)
Aug 03, 2022
Wednesday
11:30 AM - 12:30 PM
  Lecture: Reinforcement Learning
Mengdi Wang (Princeton University)
Aug 04, 2022
Thursday
10:15 AM - 11:15 AM
  Lecture: Statistical Learning Theory
Robert Schapire (Microsoft Research)
11:30 AM - 12:30 PM
  Lecture: Reinforcement Learning
Mengdi Wang (Princeton University)