15-859: Algorithms for Big Data, Fall 2017
- Instructor: David Woodruff
- Lecture time: Thursdays, 15:00-17:30 (15:00-16:10, break till 16:20, 16:20-17:30), GHC
- TA: Dhivya Eswaran
- David's office hours: Mondays, 13:00-14:00 in GHC 7217 or by appointment.
- Dhivya's recitation: Fridays, 10:30-11:20 in Baker Hall 235A
- Dhivya's office hours: Wednesdays, 10:00-11:00 in GHC 6008 or by appointment.
Grading is based on problem sets, scribing a lecture, and a presentation/project. There will be no exams.
General information about the breakdown for the grading is available
Homework solutions, scribe notes, and final projects must be typeset in LaTeX. If you are not familiar with LaTeX, see this introduction.
A template for your scribe notes is here:
- Lecture 1 slides (Least squares regression, subspace embeddings, net arguments, matrix Chernoff)
Scribe notes 1
Scribe notes 2
- Lecture 2 slides (Subsampled Randomized Hadamard Transform, Approximate Matrix Product CountSketch)
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- Lecture 3 slides (CountSketch, Affine Embeddings, Low Rank Approximation)
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- Lecture 4 slides (Sketching-based Preconditioning, Leverage Scores, Distributed Low Rank Approximation, Coresets)
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- Lecture 5 slides (Coresets, Distributed Low Rank Approximation)
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- Lecture 6 slides (L1 Regression, Cauchy Random Variables, L1 Subspace Embeddings)
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- Lecture 7 slides (Fast L1 Regression, Data Stream Model, Estimating Norms in a Stream)
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- Lecture 8 slides (Estimating p-Norms, Heavy Hitters, and Non-zero items in a Stream)
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- Lecture 9 slides (Information Theory, Distances Between Distributions, Indexing, Lower Bounds for Norms)
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- Lecture 10 slides (Information Complexity and Norm Lower Bounds in a Stream, Non-negative Matrix Factorization, Weighted Low Rank Factorization)
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- Lecture 11 slides (Weighted Low Rank Approximation, Gaussian Width, M-Estimators, Compressed Sensing)
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- Recitation 1 slides (review of linear algebra and probability)
- Many of the recitations ended up not using slides. The TA will post material used in recitations to piazza.
With the growing number of massive datasets in applications such as machine learning and numerical linear algebra, classical algorithms for processing such datasets are often no longer feasible. In this course we will cover algorithmic techniques, models, and lower bounds for handling such data. A common theme is the use of randomized methods, such as sketching and sampling, to provide dimensionality reduction. In the context of optimization problems, this leads to faster algorithms, and we will see examples of this in the form of least squares regression and low rank approximation of matrices and tensors, as well as robust variants of these problems. In the context of distributed algorithms, dimensionality reduction leads to communication-efficient protocols, while in the context of data stream algorithms, it leads to memory-efficient algorithms. We will study some of the above problems in such models, such as low rank approximation, but also consider a variety of classical streaming problems such as counting distinct elements, finding frequent items, and estimating norms. Finally we will study lower bound methods in these models showing that many of the algorithms we covered are optimal or near-optimal. Such methods are often based on communication complexity and information-theoretic arguments.
One recommended reference book is the lecturer's monograph
Sketching as a Tool for Numerical Linear Algebra.
Slide notes for about half the course are available here:
Videos from a previous course I taught on the linear algebra, l1, and weighted slides are available here:
videos . Note that mine start on 27-02-2017.
The rest of the material will be based on
the lecturer's experience and related research papers or surveys.
Materials from the following related courses might be useful in
various parts of the course:
Intended audience: The course is indended for both graduate students and advanced undegraduate students with mathematical maturity and comfort with algorithms, discrete probability, and linear algebra. No other prerequisites are required.
Maintained by David Woodruff