625.742.81 - Theory of Machine Learning
Description
This course introduces various machine learning algorithms with emphasis on their derivation and underlying mathematical theory. Topics include the mathematical theory of linear models (regression and classification), anomaly detectors, tree-based methods, regularization, fully connected neural networks, convolutional neural networks, and model assessment. Students will gain experience in formulating models and implementing algorithms using Python. Students will need to be comfortable with writing code in Python to be successful in this course. At the end of this course, students will be able to implement, apply, and mathematically analyze a variety of machine learning algorithms when applied to real-world data. Course Note(s): Although students will have coding assignments, this course differs from other EP machine learning courses in that the primary focus is on the mathematical foundations underlying the algorithms.
Instructor
Zerotti Woods
Course Structure
- o Week 1-2
- o Overview of supervised learning.
- o Review of Least Squares
- o From Least Squares to Nearest Neighbors
- o Statistical Models, Supervised Learning and Function Approximation
- o Linear models for Regression.
- o Mean Square Linear Regression
- o Ridge regression and Lasso
- o Other Sparsity Estimators (Least Angle Regression)
- o Derived Input Directions
- o Week 3-4
- o Linear model for Classification
- o Linear Regression for an Indicator Matrix
- o Linear Discriminant Analysis
- o Logistic Regression
- o Separating Hyperplanes
- o Basis Expansions and Regularization
- o Piecewise Polynomials and Splines
- o Natural Cubic Splines
- o Smoothing splines
- o Week 5-6
- o Basis Expansions and Regularization
- o Degrees of freedom
- o Automatic selection of smoothing parameters
- o Nonparametric logistic regression
- o Model Assessment
- o Bias, Variance, and Model Complexity
- o Optimism of the Training Error Rate
- o Estimate of In-Sample Prediction Error
- o Effective Number of Parameters
- o Week 7
- o Model assessment.
- o The Bayesian Approach and BIC
- o Minimum Description Length
- o Vapnik–Chervonenkis Dimension
- o Cross Validation
- o Week 8
- o Project Proposals
- o Week 9-10
- o Neural Networks
- o Differential and Backpropagation
- o Stochastic Gradient Descent
- o Generative Adversarial Networks
- o Week 11
- o Neural Networks
- o CNNs (various kinds)
- o Regularization
- o Weight Decay
- o L1
- o Dropout
- o Neural Networks
- o Week 12-13
- o Tree based methods.
- o Generalized additive models
- o Tree based methods
- o PRIM
- o MARS
- o Boosting
- o Boosting methods
- o Loss functions and robustness
- o Numerical optimization via gradient boosting
- o Regularization
- o Interpretation
- o Week 14
- o Anomaly Detectors
- o Unsupervised Learning
- o Cluster analysis
- o Principal Component Analysis
- o Kernel PCA
- o Basis Expansions and Regularization
- o Linear model for Classification
- o Overview of supervised learning.
Course Topics
- Linear Models (Regression)
- Linear Models (Classification)
- Anomaly Detectors
- Tree based methods
- Boosting
- Regularization,
- Neural Networks,
- Model Assessment
Course Goals
This course covers mathematical principles that serve as a basis for machine learning algorithms. Emphasis in this course will be on formulating mathematical problems that can be solved using machine learning, understanding which algorithms are appropriate for different data sets, and proper uses of machine learning algorithms to explore real world problems
Course Learning Outcomes (CLOs)
- Learn mathematical theory that underline modern machine learning algorithms.
- Explore which algorithms may be suited for different real-world dataset.
- Discuss current research and explore novel machine learning algorithms.
Textbooks
Hastie, T., Friedman, J., & Tisbshirani, R. (2017). The Elements of statistical learning: data mining, inference, and prediction. Springer.
ISBN 978-0-387-84857-0
Required Software
Python
You will need access to a recent version of Python. Anaconda is an open source python distribution platform that contains all packages and libraries that will be needed for this course.
Student Coursework Requirements
It is expected that each student participate in all lectures. All lectures will be recorded so in the event that a student must be absent, the lecture recording will be posted.
This course will consist of the following basic student requirements:
Homework 18%
|
Discussion Post for Weekly Research Paper 12%
|
Group Research Assignment 20%
|
Final Project 40%
|
Individual Research Paper 10%
|
Grading Policy
A grade of A indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week.
A grade of B indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course.
EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).
| Score Range | Letter Grade |
|---|---|
| 100-98 | = A+ |
| 97-94 | = A |
| 93-90 | = A− |
| 89-87 | = B+ |
| 86-83 | = B |
| 82-80 | = B− |
| 79-77 | = C+ |
| 76-73 | = C |
| 72-70 | = C− |
| 69-67 | = D+ |
| 66-63 | = D |
| <63 | = F |
Course Policies
Homework will be assigned for the first half of the course. It will be due BEFORE the beginning of class on the day it is due. Students will be given a problem set that has that has ten questions. Students are encouraged to discuss with other students about the HW assignments
Presentations on chosen dataset will be during the 8 and 9th week of class. Each group will have twelve minutes to present with a three minute question and answering period. Students in the audience along with the instructor will give formal feedback on every presentation.
Final presentations will be done during finals week. Each group will have twenty five minutes to present with a five minute question and answer period. Students in the audience along with the instructor will give formal feedback on every presentation.
Students have a responsibility to assist in peer reviewing. This is an essential component to the course and students are expected to participate during each presentation.
Prerequisites
Multivariate calculus, linear algebra (e.g. EN.625.252), and probability and statistics (EN.625.603 or similar course). Students should also be comfortable with reading and writing mathematical proofs.
Academic Policies
Deadlines for Adding, Dropping and Withdrawing from Courses
Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.
Academic Misconduct Policy
All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.
This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.
Students with Disabilities - Accommodations and Accessibility
Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.
For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.
Student Conduct Code
The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically.
For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/
Classroom Climate
JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity.
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).
Course Auditing
When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.