15-859: Algorithms for Big Data, Fall 2019
- Instructor: David Woodruff
- Lecture time: Thursdays, 15:00-17:30 (15:00-16:10, break till 16:20, 16:20-17:30), GHC 4303.
- TA: Rajesh (Raj) Jayaram
- David's office hours: Tuesdays, 13:00-14:00 in GHC 7217 or by appointment.
- Raj's recitation: Fridays, 9:30-10:30 in GHC 4303, starting Sep 6.
- Raj's office hours: Wednesdays, 10:00-11:00 in GHC 5105 or by appointment.
- Piazza site: piazza.com/cmu/fall2019/15859/home
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)
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- 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)
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- Lecture 7 slides (Data Stream Model, Estimating Norms in a Stream)
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- Lecture 8 slides (Heavy Hitters, 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)
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- Lecture 11 slides (NMF, Weighted Low Rank Approximation, Gaussian Width, M-Estimators, Compressed Sensing)
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Related additional notes
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.
Some videos from a shorter version of this course I taught are available here:
videos . Note that mine start on 27-02-2017.
This course was previously taught at CMU in Fall 2017
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