CSC 246/446, Spring 2009
Mathematical Foundations of Artificial Intelligence
Time: TR 11:0512:20,
Place: CSB 601
Books
Required:

[B] Christopher M. Bishop, Pattern Recognition and Machine Learning.
Recommended:

[HTF] Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd edition), 2009

[KV] Michael J. Kearns and Umesh V. Vazirani, An Introduction to Computational Learning Theory, 1994.

[M] Tom Mitchell, Machine Learning, 1997.

[DHS] Richard O. Duda, Peter E. Hart, and David G. Stork, Pattern Classification (2nd edition), 2001.

[DGL] Luc Devroye, Laszlo Gyorfi, Gabor Lugosi, A Probabilistic Theory of Pattern Recognition, 1996.

[W] Larry Wasserman, All of Statistics, 2004.

[A] Ethem Alpaydin, Introduction to Machine Learning, 2004.
Homework
 due Jan. 27 (Tu)  basic 1
 [B] 1.3, 1.5, 1.6, 1.7, 1.11, 1.30, 1.31, 1.32, 1.33.
 due Feb. 3 (Tu)
 [B] 2.8, 2.14, 2.26, 3.3, 4.5.
 due Feb. 26 (Th)
 [B] 8.8, 8.9, 8.10.
 Prove the following theorem: Let G be an undirected graphical model.
Let A,B,C be sets of vertices such that B separates A from C. Then
X_A is independent from X_C conditioning on X_B.
 due Mar. 24 (Tu)
 [KV1.1] Let C be the class of axisalligned rectangles in R^n. Show that C is efficiently PAC learnable.
 Let C be the class of unions of 3 intervals in R. Show that C is efficiently PAC learnable.
 [KV2.1] Show tht for each k there exists a function that can be represented as a kdecision list, but not by a kCNF or kDNF formula.
 due Apr. 14 (Tu)
 due Apr. 21 (Tu)
Projects
 due Feb. 5 (Th)  estimation.
 due Feb. 15 (Su)  SVM's.
 due Mar. 3 (Tu)  EM.
 due Apr. 23 (Th)  MDP's
Lecture plan (tentative)

Jan. 15 (Th) Introduction.
 TOPICS: kNN, generalization error, true error, crossvalidation, entropy, decision trees.
 READING: [M] 3,5.

Jan. 20 (Tu) Probability theory review.
 TOPICS: density, expectation, variance, conditional expectation, covariance, basic densities.
 READING: [B] 1.

Jan. 22 (Th) Bayesian inference.
 TOPICS: frequentist/bayesian viewpoint, likelihood, Bayes theorem, conjugate priors, maximum likelihood.
 READING: [B] 2, [HTF] 2.

Jan. 27 (Tu) (Linear) regression.
 TOPICS: curve fitting, regularization, least squares (connection with maximum likelihood).
 READING: [B] 3, [HTF] 3.

Jan. 29 (Th) (Linear) classification.
 TOPICS: perceptron algorithm.
 READING: [B] 4, [HTF] 4.

Feb. 3 (Th) SVM I.

Feb. 5 (Tu) SVM II.

Feb. 10 (Tu) Neural Networks.
 TOPICS: neural networks, backpropagation.
 READING: [B] 5.1,5.2,5.3.

Feb. 12 (Th) Graphical models I.

Feb. 17 (Tu) Graphical models II.
 TOPICS: sumproduct, maxsum algorithms, belief propagation.
 READING: [B] 8.

Feb. 19 (Th) EM algorithm.
 TOPICS: mixture models, EM algorithm.
 READING: [B] 9.

Feb. 24 (Tu) Sampling I.
 TOPICS: sampling from basic distributions, rejection sampling.
 READING: [B] 11.1.

Feb. 26 (Th) Sampling II.
 TOPICS: MCMC.
 READING: [B] 11.2, 11.3, 11.4.

Mar. 3 (Tu) review

Mar. 5 (Th) EXAM

Mar. 10 Tu SPRING BREAK

Mar. 12 Th SPRING BREAK

Mar. 17 (Tu) Theory I  PAC.
 TOPICS: Chernoff bound, union bound, PAC.
 READING: [KV] 1,2.

Mar. 19 (Th) Theory II  VCdimension.
 TOPICS: VC dimension.
 READING: [KV] 3.

Mar. 24 (Tu) Theory III  boosting.

Mar. 26 (Th) Theory IV  membership queries.

Mar. 31 (Tu) PCA I.
 TOPICS: PCA, SVD
 READING: [B] 12.1

Apr. 2 (Th) PCA II.
 TOPICS: ICA
 READING: [B] 12.4.1

Apr. 7 (Tu) Manifold learning.

Apr. 9 (Th) Hidden Markov Models I.
 TOPICS: HMMs, Viterbi algorithm.
 READING: [B] 13.1, 13.2.

Apr. 14 (Tu) Hidden Markov Models II.

Apr. 16 (Th) Reinforcement learning I.

Apr. 21 (Tu) Reinforcement learning II.
 TOPICS: Value Iteration (proof of correctness), POMDP's.
 READING: [B] 14.

Apr. 23 (Th) review

Apr. 28 (Tu) EXAM
Grading
 Homework: 20%,
 Projects: 20%,
 EXAM 1: 30%,
 EXAM 2: 30%.
Homework/Project Rules
 Homework is collected on the due date, before class.
 No late homework will be accepted without instructor's permission (a permission must be requested at least 24 hours before the due date).
 In the final evaluation everybody's one lowest homework score and one lowest project score
will be dropped.
 You may work with other people on the homework, but you must each write up your solutions separately
(without any written aid, for example, looking at other people's source code (or written up solution)
is forbidden). If you work with other people, indicate who you worked with on your solution.