15-859(A) Machine Learning Theory, Spring 2004

15-859(A) MACHINE LEARNING THEORY

Instructor: Avrim Blum

Time: TR 1:30-2:50

Place: Wean 5409

Course description: This course will focus on theoretical aspects of machine learning. We will examine questions such as: What kinds of guarantees can one prove about learning algorithms? What are good algorithms for achieving certain types of goals? Can we devise models that are both amenable to mathematical analysis and make sense empirically? What can we say about the inherent ease or difficulty of learning problems? Addressing these questions will require pulling in notions and ideas from statistics, complexity theory, information theory, cryptography, game theory, and empirical machine learning research.

Text: An Introduction to Computational Learning Theory by Michael Kearns and Umesh Vazirani, plus papers and notes for topics not in the book.

Office hours: Just stop by my office or make an appointment.

Note: This is the 2004 version of the Machine Learning Theory course. For the 2007 version, click here.

Handouts

Lecture Notes

01/13: Introduction, basic definitions, the consistency model.
01/15: The Mistake-bound model, relation to consistency, halving and Std Opt algorithms.
01/20: The weighted majority algorithm (combining "expert" advice) & applications.
01/22: The Perceptron and Winnow algorithms.
01/27: The PAC model: basic results and Occam's razor.
01/29: Uniform convergence, Chernoff/Hoeffding bounds, MB=>PAC, greedy set-cover. Handout on Tail inequalities.
02/03: VC-dimension. Proof of Sauer's lemma. slides and notes.
02/05: VC-dimension, contd. Proof of main thm.
02/10: Boosting I: weak vs strong learning, basic issues, Schapire's original algorithm.
02/12: Boosting II: Adaboost. Use as proof of Hoeffding bounds.
02/17: Learning from noisy data. SQ model intro.
02/19: SQ => PAC + noise. SQ-dimension. Begin hardness results for SQ algorithms.
02/24: Characterizing SQ learnability with Fourier analysis, contd. (same notes as last time)
02/26: Weak-learning of monotone functions.
03/02: Membership queries I: basic algorithms (monotone DNF, log-n var functions); begin KM for finding large fourier coeffs.
03/04: Membership queries II: finish KM algorithm. Fourier spectrum of Decision Trees and DNF.
03/16: Membership queries III: Bshouty's alg for decision trees and XOR-of-terms. Cryptographic lower bounds.
03/18: Angluin's algorithm for learning DFAs (ppt). More notes.
03/23: Learning finite-state environments without a reset. Also slides.
03/25: MDPs and reinforcement learning.
03/30: More on MDPs. (short class today)
04/01: Kalai-Vempala algorithm for online optimization.
04/06: Maxent and maximum-likelihood exponential models. Connection to winnow.
04/08: Sham Kakade guest lecture: Deterministic Calibration and Nash Equilibrium
04/13: Linear separators, Margins, & Kernels.

Additional Readings

(Related papers that go into more detail on topics discussed in class)

Online Learning

Nick Littlestone, Learning Quickly when Irrelevant Attributes Abound: A New Linear-threshold Algorithm. Machine Learning 2:285--318, 1987. (The version pointed to here is the tech report UCSC-CRL-87-28.) This is the paper that first defined the Mistake-bound model, and also introduced the Winnow algorithm. A great paper.
Littlestone and Warmuth, The Weighted Majority Algorithm. Information and Computation 108(2):212-261, 1994. (The version pointed to here is the tech report UCSC-CRL-91-28.) Introduces the weighted majority algorithm, along with a number of variants. Also a great paper.
Nicolò Cesa-Bianchi, Yoav Freund, David Haussler, David P. Helmbold, Robert E. Schapire, and Manfred K. Warmuth. How to use expert advice. Journal of the ACM, 44(3):427-485, May 1997. Continuing on with line of research in the [LW] paper, this gives tighter analyses of multiplicative-weighting expert algorithms and addresses a number of issues.
Yoav Freund and Robert E. Schapire. Adaptive game playing using multiplicative weights. Games and Economic Behavior, 29:79-103, 1999.
Avrim Blum, On-Line Algorithms in Machine Learning (a survey). From "Online Algorithms: the state of the art", Fiat and Woeginger eds., LNCS #1442, 1998.
Adam Kalai and Santosh Vempala, Efficient algorithms for the online decision problem, COLT '03. Earlier version (a little simpler and closer to notation used in class): Follow the Leader for Online Optimization.

PAC model

My FOCS'03 tutorial on Machine Learning Theory
David Haussler Chapter on PAC learning model, and decision-theoretic generalizations, with applications to neural nets. From Mathematical Perspectives on Neural Networks, Lawrence Erlbaum Associates, 1995, containing reprinted material from "Decision Theoretic Generalizations of the PAC Model for Neural Net and Other Learning Applications", Information and Computation, Vol. 100, September, 1992, pp. 78-150. This is a really nice survey of the PAC model and various sample-complexity results.

Boosting

The original paper: Yoav Freund and Rob Schapire, A decision-theoretic generalization of on-line learning and an application to boosting, Journal of Computer and System Sciences, 55(1):119-139, 1997.
A recent overview by Rob Schapire: The boosting approach to machine learning: An overview. In MSRI Workshop on Nonlinear Estimation and Classification, 2002.

Fourier analysis, weak learning, SQ learning

Avrim Blum, Merrick Furst, Jeffrey Jackson, Michael Kearns, Yishay Mansour, and Steven Rudich, Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis., STOC '94 pp. 253--262.
Y. Mansour. Learning Boolean Functions via the Fourier Transform. Survey article in ``Theoretical Advances in Neural Computation and Learning", 391--424 (1994).
A. Blum, C. Burch, and J. Langford, On Learning Monotone Boolean Functions. Proceedings of the 39th Annual Symposium on Foundations of Computer Science (FOCS '98).

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