EE596B - Submodular Functions, Optimization, and Applications to Machine Learning, Spring Quarter, 2016
Last updated: $Id: index.html 2028 2016-06-03 17:13:54Z bilmes $
This page is located at http://www.ee.washington.edu/people/faculty/bilmes/classes/ee596b_spring_2016/.
A version of this class was taught previously, and its contents and slides can be found at http://j.ee.washington.edu/~bilmes/classes/ee596b_spring_2014/
Instructor:
Prof. Jeff A. Bilmes --- Email meOffice: 418 EE/CS Bldg., +1 206 221 5236
Office hours: TBD, EEB-418 (+ online)
TA
Kai Wei (kaiwei@uw.edu)Office: EEB-417
Office hours: TBD
Time/Location
Class is held: Mon/Wed 1:30-3:30, Loew Hall, Room 116.Announcements
- Sticky: Almost all of the announcements, homework postings, homework solutions, and electronic discussion for our class are going to be posted on canvas, and can be found at this link. However, do see the youtube videos below and you can see absolutely everything.
Submodular Functions, Optimization, and Applications to Machine Learning
Description: This class will be a thorough introduction to submodular functions.
This class will be a thorough introduction to submodular functions. Applications of submodularity are vast, and include areas in in computer vision, constraint satisfaction, game theory, social networks, economics, information theory, structured convex norms, natural language processing, sensor networks, graphical models and probabilistic inference, and other areas of machine learning. Submodularity is a good model for cooperation, complexity, and attractiveness as well as for diversity, coverage, and information.
In this class, we will learn about a variety of properties of submodularity and supermodularity. Motivated by applications, we'll cover submodularity's definitions, its properties, the many operations that preserve submodularity, variants and extensions of submodularity, and certain special submodular functions, and computational properties. The goal of this section will be to develop a deep intuitive understanding of both submodular and supermodular functions.
Other topics we will overview include: the theory of matroids and lattices, polyhedral properties of submodular functions, subdifferentials and superdifferentials, the Lovasz extension (i.e., the Choquet integral) of submodular functions and convex and concave extensions in general.
As for submodular optimization, we'll discuss submodular maximization algorithms in the unconstrained and constrained (i.e., knapsack, matroid, combinatorial, etc.) cases, the ever important greedy algorithm and its uses. For submodular minimization, we'll give a history of submodular minimization, including both numerical and combinatorial algorithms, computational properties of these algorithms, and descriptions of both known results and currently open problems in this area (as well as discuss both unconstrained and constrained cases).
Other problems we'll discuss include submodular cover problems, submodular flow problems, the principle partition of a submodular function and its variants. We'll see, for example, how submodularity can be used to solve non-submodular problems, for example difference of submodular programs, and submodular relaxation strategies.
Homework
Homework must be done and submitted electronically via the following link https://canvas.uw.edu/courses/1039754/assignments.Lecture Slides
Lecture slides will be made available as they are being prepared --- they will probably appear soon before a given lecture, and they will be in PDF format (original source is latex). Note, that these slides are corrected after the lecture (and might also include some additional discussion we had during lecture). If you find bugs/typos in these slides, please email me. The slides are available as "presentation slides" and also in (mostly the same content) 2-up form for printing. After lecture, the marked up slides will appear under the "presented slides" column (and might include typo fixes, ink corrections, and other little notes/discussions/drawings that occured during class).| Lec. # | Slides | 2-Up Slides | Lecture Date | Last Updated | Contents | Presented Slides | Video |
| 1 | 3/28/2016 | 3/28/2016 | Logistics, Motivation, Applications. | ||||
| 2 | 3/30/2016 | 3/30/2016 | Machine Learning Apps (diversity, complexity, parameter, learning target, surrogate). | ||||
| 3 | 4/4/2016 | 4/4/2016 | Info theory exs, more apps, definitions, graph/combinatorial examples, matrix rank example, visualization | ||||
| 4 | 4/6/2016 | 4/6/2016 | Graph and combinatorial examples, matrix rank, Venn diagrams, examples of proofs of submodularity, some useful properties | ||||
| 5 | 4/11/2016 | 4/11/2016 | Examples and Properties, Other Defs., Independence | ||||
| 6 | 4/18/2016 | 4/18/2016 | Independence, Matroids, Matroid Examples, Matroid Rank is submodular | ||||
| 7 | 4/20/2016 | 4/20/2016 | Matroid Rank, More on Partition Matroid, System of Distinct Reps, Transversals, Transversal Matroid, Matroid and representation, Dual Matroid | ||||
| 8 | 4/25/2016 | 4/25/2016 | Transversals, Matroid and representation, Dual Matroids | ||||
| 9 | 4/27/2016 | 4/27/2016 | Dual Matroids, Properties, Combinatorial Geometries, Matroid and Greedy | ||||
| 10 | 5/2/2016 | 5/2/2016 | Matroid and Greedy, Polyhedra, Matroid Polytopes, Polymatroid | ||||
| 11 | 5/9/2016 | 5/9/2016 | From Matroids to Polymatroids, Polymatroids | ||||
| 12 | 5/11/2016 | 5/11/2016 | Polymatroids, Polymatroids and Greedy | ||||
| 13 | 5/16/2016 | 5/16/2016 | Polymatroids and Greedy; Possible Polytopes; Extreme Points; Polymatroids, Greedy, and Cardinality Constrained Maximization | ||||
| 14 | 5/18/2016 | 5/18/2016 | Cardinality Constrained Maximization; Curvature; Submodular Max w. Other Constraints | ||||
| 15 | 5/23/2016 | 5/23/2016 | Submodular Max w.\ Other Constraints, Most Violated $\leq$, Matroids cont., Closure/Sat, | ||||
| 16 | 5/25/2016 | 5/25/2016 | Closure/Sat, Fund.\ Circuit/Dep, | ||||
| 17 | 5/25/2016 | 5/25/2016 | Min-Norm Point and SFM, Min-Norm Point Algorithm, Proof that min-norm gives optimal. | ||||
| 18 | 6/3/2016 | 6/3/2016 | Proof that min-norm gives optimal, Lovasz extension. | ||||
| Lec. # | Slides | 2-Up Slides | Lecture Date | Last Updated | Contents | Presented Slides | Video |
Discussion Board
You can post questions, discussion topics, or general information at this link.
Relevant Books
There are many books available that discuss some the material that we are covering in this course. Some good books are listed below, but see the end of the lecture slides for books/papers that are relevant to each specific lecture. There are many books available that discuss some the material that we are covering in this course. See the end of the lecture slides for books and papers that are relevant to that specific lecture, and see lecture1.pdf for a list of general texts that are relevant to this class. Other books are below, but note that for some of the material, the best reference is the slides themselves.- Fujishige, "Submodular Functions and Optimization", 2005
- Narayanan, "Submodular Functions and Elecrical Networks", 1997
- Welsh, "Matroid Theory", 1975.
- Oxley, "Matroid Theory", 1992 (and 2011).
- Lawler, "Combinatorial Optimization: Networks and Matroids", 1976.
- Schrijver, "Combinatorial Optimization", 2003
- Gruenbaum, "Convex Polytopes, 2nd Ed", 2003.
- See lecture 1 slides for most relevant texts.
Important Dates/Exceptions (also see this academic calendar).
- Monday, 5/30, no class (holiday, Memorial day).
- Monday, 6/6, final presentations in class.
Alternative Contact
If you must, you can send me or the TA anonymous email