Description

The course assumes students are comfortable with analysis, probability, statistics, and basic programming. This course will cover core concepts in machine learning and statistical inference. The ML concepts covered are spectral methods (matrices and tensors), non-convex optimization, probabilistic models, neural networks, representation theory, and generalization. In statistical inference, the topics covered are detection and estimation, sufficient statistics, Cramer-Rao bounds, Rao-Blackwell theory, variational inference, and multiple testing. In addition to covering the core concepts, the course encourages students to ask critical questions such as: How relevant is theory in the age of deep learning? What are the outstanding open problems? Assignments will include exploring failure modes of popular algorithms, in addition to traditional problem-solving type questions.

General Information

Outline
Lecture 1: Introduction, Probability

Lecture 2: Sufficient statistics

Lecture 3: Bayesian

Lecture 4: Neyman Pearson

Lecture 5: Sequential detection

Lecture 6: Estimation and UMVU

Lecture 7: Cramer Rao

Lecture 8: Midterm exam

Lecture 9: Spectral Methods: PCA/CCA, HMM

Lecture 10: Spectral Methods: Tensor methods, method of moments

Lecture 11: Optimization: Non-convex

Lecture 12: Optimization in deep learning: Adam, CGD, MAdam

Lecture 13: generalization theory

Lecture 14: generalization theory

Lecture 15: approximation theory

Lecture 16: operator learning

Lecture 17: operator learning 

Final presentation: Saturday 9am-1pm, March 18th.
Location
ANB 213
Time
Class: Tuesday, Thursday 13:00-14:25
Office hour: TBD
Grading
Homework Assignments 30%
Project 50%
Quiz 20% (1 in-class quiz)
Recitation schedule
Week 1: software tool
Week 2: probability
Week 3: statistics
Week 4: linear algebra
Week 5: tensor

Announcements

Announcements are not public for this course.
Staff Office Hours
NameOffice Hours
Anima Anandkumar
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Jiawei Zhao
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Zongyi
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Kaiyu Yang
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Peter Wang
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Julius
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Bahareh Tolooshams
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Rafal
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