I do not have an office at NYU. I work from home. I come to NYU only to give lectures. If you need to contact me, please email me and/or arrange a Zoom or Google Hangouts call. Office hours are on Zoom.>
In this course you will learn the theoretical foundations of machine learning. We will explain how a machine learning algorithm can make accurate predictions on unseen data. This property is called generalization. We develop a statistical theory of generalization for prediction problems. Along the way we analyze some popular machine learning methods (support vector machines, boosting, perceptron, stochastic gradient descent, decision trees, neural networks, k-nearest neighbor). Besides generalization properties of machine learning algorithms, we will look also at their computational complexity and computational hardness of the underlying optimization problems.
The class will be completely theoretical. In lectures, I will give definitions and prove theorems. In homeworks and exams, I will ask you to solve mathematical problems and prove theorems. You will NOT do any coding, you will NOT do any data analysis, and you will NOT build any machine learning models.
You must have taken courses in probability theory, linear algebra, and algorithms. You will benefit from prior exposure to machine learning (ML) (e.g. introductory ML course, neural network course, statistical inference course, practical experience). However, knowledge of ML is not a prerequisite. I will give a brief introduction to ML in the first lecture.
I expect you to know one-dimensional calculus (limits, infimum, supremum, continuity, derivatives and integrals), mathematical notation (sets, functions, logical formulas), and elementary combinatorics (combinations, permutations, binomial coeficients). You must be comfortable doing mathematical proofs.
Note that the total percentage adds up to 110%. That means you can make up lost points. If you want to do well in the course, make sure to submit solutions to all homework problems.
There is one 2.5 hour class meeting per week, divided by a 15 minute break. In accordance with NYU guidelines, you must wear a mask covering your face and nose whenever you are attending lecture.
Your solution must be turned both by email and as a printed out hard-copy in class by the due date. Send emails to email@example.com with subject "Homework #?". Use LaTeX and submit your solution as a PDF file. Use the following template.
|LaTeX source||Handout date||Due date||Graded by||Solution PDF||Soltion LaTeX source|
|Homework #0||LaTeX source||January 25||February 1||February 6|
|Homework #1||LaTeX source||February 6||February 20||February 27||Solution PDF||Solution LaTeX source|
|Homework #2||LaTeX source||February 20||March 6||March 13||Solution PDF||Solution LaTeX source|
|Homework #3||LaTeX source||March 27||April 10||April 17||Solution PDF||Solution LaTeX source|
|Homework #4||LaTeX source||April 10||April 24||April 31||Solution PDF||Solution LaTeX source|
I am hoping to cover the topics listed below. Additional topics (decision trees, k-nearest neighbor, neural networks) might be added if time permits.
|Week 1||January 30||Generalization error, Test error, Optimal Bayes classifier||Chapters 1,2,3|
|Week 2||February 6||Empirical Risk Minimization (ERM), Overfitting, PAC model with finite hypothesis class, Hoeffding's bound||Chapters 2,3,4; Appendix B|
|Week 3||February 13||Hoeffding's bound, PAC model, No free lunch theorem||Chapters 3,4,5; Appendix B|
|Week 4||February 20||VC dimension, Sauer's lemma, Radon's theorem, VC dimension of halfspaces, epsilon-nets, epsilon-approximations||Chapter 6|
|Week 5||February 27||epsilon-nets, epsilon-approximations, sample complexity upper and lower bounds||Chapters 6,28|
|Week 6||March 6||Measure theory, Upper bound on the sample complexity for Agnostic PAC model||Chapters 6, 28|
|Week 7||March 13||Midterm exam|
|Week 8||March 20||Spring break — No lectures|
|Week 9||March 27||Non-uniform learning and computational complexity of learning||Chapters 7, 8|
|Week 10||April 3||Online learning model, Halving algorithm, Mistake bound, Perceptron, Winnow, Online-to-batch conversion||Chapter 21|
|Week 11||April 10||Hedge, Perceptron, Online-to-batch conversion, Boosting||Chapters 21, 10|
|Week 12||April 17||Boosting, Decision trees||Chapters 10, 18|
|Week 13||April 24||Least squares, logistic regression, convex learning problems||Chapters 9, 12|
|Week 14||May 1||Convex learning problems, stability, regularization||Chapters 12, 13|
|Week 15||May 8||Regularization stability, Online gradient descent, stochastic gradient descent||Chapters 13, 14|
|Week 16||May 15||Final exam|