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Summer Graduate School

Mathematics of Big Data: Sketching and (Multi-) Linear Algebra (Virtual School) June 21, 2021 - July 02, 2021
Parent Program: --
Location: MSRI: Simons Auditorium, Commons Room
IBM
Organizers LEAD Kenneth Clarkson (IBM Research Division), Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University), Tamara Kolda (Sandia National Laboratories; MathSci.ai), Shashanka Ubaru (IBM Thomas J. Watson Research Center)
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Teaching Assistants(s)

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Description
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This summer school will introduce graduate students to sketching-based approaches to computational linear and multi-linear algebra. Sketching here refers to a set of techniques for compressing a matrix, to one with fewer rows, or columns, or entries, usually via various kinds of random linear maps. We will discuss matrix computations, tensor algebras, and such sketching techniques, together with their applications and analysis.

School Structure

There will be two lectures per day. There will be a problem session in the morning after Lecture 1, and one in the afternoon after Lecture 2. The problem sessions will generally be led by the Teaching Assistants, though the Lecturers will be involved to observe or lead discussion as well. The purpose of the sessions is to reinforce and deepen students’ understanding of the material from the lectures by working on problems and in certain cases, to discuss material relevant to future lectures. This will be done by discussion, question-and-answer, and problem-solving from problem sets. Activities may include presentation of solutions to problems assigned based on lectures, student or TA presentation of material relevant to lecture, or exercises and presentation of relevant background material. 

Suggested Prerequisites

The minimum requirement for students to beneficially participate in this summer schools are the basics of probability, algorithms, linear algebra.

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

Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Linear and Non-linear Algebra

  • Robust Estimation

  • Optimization Methods for AI

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Schedule, Notes/Handouts & Videos
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Jun 21, 2021
Monday
09:00 AM - 10:15 AM
  Introduction, Algorithmic Motivation
Kenneth Clarkson (IBM Research Division)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  Oblivious Subspace Embeddings
Kenneth Clarkson (IBM Research Division)
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups
Jun 22, 2021
Tuesday
09:00 AM - 10:15 AM
  Mathematics of Big Data- Sketching and (Multi-) Linear Algebra- Lecture 2
Kenneth Clarkson (IBM Research Division)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  Mathematics of Big Data- Sketching and (Multi-) Linear Algebra- Lecture 3
Kenneth Clarkson (IBM Research Division)
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups
Jun 23, 2021
Wednesday
09:00 AM - 10:15 AM
  Mathematics of Big Data- Sketching and (Multi-) Linear Algebra- Lecture 4
Kenneth Clarkson (IBM Research Division)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  Mathematics of Big Data- Sketching and (Multi-) Linear Algebra- Lecture 5
Kenneth Clarkson (IBM Research Division)
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups
Jun 24, 2021
Thursday
09:00 AM - 10:15 AM
  Mathematics of Big Data- Sketching and (Multi-) Linear Algebra- Lecture 6
Kenneth Clarkson (IBM Research Division)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  Mathematics of Big Data- Sketching and (Multi-) Linear Algebra- Lecture 7
Kenneth Clarkson (IBM Research Division)
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups
Jun 25, 2021
Friday
09:00 AM - 10:15 AM
  Mathematics of Big Data- Sketching and (Multi-) Linear Algebra- Lecture 8
Shashanka Ubaru (IBM Thomas J. Watson Research Center)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  Mathematics of Big Data- Sketching and (Multi-) Linear Algebra- Lecture 9
Shashanka Ubaru (IBM Thomas J. Watson Research Center)
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups
Jun 28, 2021
Monday
09:00 AM - 10:15 AM
  CP Tensor Decomposition
Tamara Kolda (Sandia National Laboratories; MathSci.ai)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  CP Tensor Decomposition 2
Tamara Kolda (Sandia National Laboratories; MathSci.ai)
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups
Jun 29, 2021
Tuesday
09:00 AM - 10:15 AM
  Kronecker FJLT
Tamara Kolda (Sandia National Laboratories; MathSci.ai)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  Sketching for Sparse CP & Efficient Computations
Tamara Kolda (Sandia National Laboratories; MathSci.ai)
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups
Jun 30, 2021
Wednesday
09:00 AM - 10:15 AM
  Lecture 1
Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  Lecture 2
Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University)
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups
Jul 01, 2021
Thursday
09:00 AM - 10:15 AM
  Matrix Mimetic Tensor Algebra Applications & M-Matrix Mimetic Tensor Algebra
Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  Matrix Mimetic Tensor Algebra Applications 2
Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University)
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups
Jul 02, 2021
Friday
09:00 AM - 10:15 AM
  Lecture 9 Dimensionality Reduction for Tukey Regression Sub-Gaussians
Kenneth Clarkson (IBM Research Division)
10:15 AM - 10:30 AM
  Break
10:30 AM - 12:00 PM
  Working Groups
12:00 PM - 01:00 PM
  Break
01:00 PM - 02:15 PM
  Lecture
02:15 PM - 02:30 PM
  Break
02:30 PM - 04:00 PM
  Working Groups