CS/ECE 861 Theoretical Foundations of Machine Learning

Fall 2021 Course: Description Advanced mathematical theory and methods of machine learning. Statistical learning theory, Vapnik-Chevronenkis Theory, model selection, high-dimensional models, nonparametric methods, probabilistic analysis, optimization, learning paradigms. Prereq CS/ECE 761 or ECE 830 (While not required, my suggested course sequence for incoming machine learning graduate students is CS 532 Matrix Methods in Machine Learning - CS 761 - CS 861. In addition, Math 521 Analysis I, ECE 730 Modern Probability Theory and Stochastc Processes, CS/ECE 524 Introduction to Optimization, and similar math courses are helpful) Instructor Professor Jerry Zhu, jerryzhu@cs.wisc.edu Exam Midterm exam: Friday Oct. 8 (in class) Final exam: Friday Nov. 12 (in class) Exam grading questions must be raised with the instructor within one week after it is returned. Project An open machine learning project, done in groups of two. Requires an analysis component. Project proposal due: Nov. 19 (Friday). One page pdf Project report due: Dec. 15 (Wednesday). Eight page pdf in NeurIPS format. Topics Supervised Learning Probabily Approximately Correct (PAC) [SS] Ch 2, 3, 4 Rademacher complexity, Growth function, VC dimension [SS] Ch 6, 26 Convexity, stability and generalization [SS] Ch 9, 13 Occam's razor, PAC-Bayesian [SS] Ch 7, 31 Online learning Mistake bound, halving algorithm, Online perceptron algorithm [SS] Ch 21 Expert advice, Hedge [Slivkins] Chapter 5 Multi-armed bandits Adversarial bandits: EXP3 [LS] Chapters 1, 11 Stochastic bandits: ETC, UCB, successive elimination [LS] Chapters 5, 6, 7 Contextual bandits, LinUCB [LS] Chapters 18, 19 Minimax lower bound [LS] Chapters 13, 14, 15 Reinforcement learning UCB-VI [AJKS] Ch 1, 6, 7 References [AJKS] Alekh Agarwal, Nan Jiang, Sham M. Kakade, Wen Sun. Reinforcement Learning: Theory and Algorithms [SS] Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning: From Theory to Algorithms [LS] Tor Lattimore and Csaba Szepesvari. Bandit Algorithms. [Slivkins] Aleksandrs Slivkins. Introduction to Multi-Armed Bandits Grading: Homework (40%), exam (40%), project (20%). Class learning outcome Student will be able to: - derive sample complexity bounds using concentration of measure inequalities - analyze bias-variance tradeoffs and model selection criteria - derive rates of convergence for nonparametric machine learning algorithms - gain familiarity with various machine learning paradigms, including supervised, unsupervised, active, multitask, and online learning.