Effective Algorithms in Machine Learning and Statistics (CSCI599)

Spring 2016

This course is a graduate introduction to the algorithmic aspects of machine learning and statistics. Our focus will be on the design and analysis of statistically and computationally efficient inference algorithms in well-defined learning models.

The first part of the course will survey recent algorithmic techniques in the context of unsupervised learning. The goal of unsupervised learning is to discover hidden structure in a set of unlabeled data. We will study algorithms for learning probability distributions in various settings (shape restricted distributions, mixture models, latent variable models, topic models).

The second part of the course will focus on algorithmic problems in supervised learning. The goal of supervised learning is to infer a function from a set of labeled observations. More specifically, we will study algorithms for learning Boolean functions from labeled examples in a number of models (online learning, PAC learning, SQ learning, learning with noise, etc.).

The course is primarily targeted toward graduate students who want to gain familiarity with mathematical and algorithmic tools for the analysis of large datasets. Advanced undergraduate students with sufficient mathematical maturity are welcome (subject to instructor's approval).

Course Information

Instructor: Ilias Diakonikolas

Teaching Assistant: Li Han

Lectures: Wednesdays 14:00-17:20, THH 215.

Prerequisites

Mathematical maturity. Solid background in algorithms, linear algebra, and probability.

Course Outline

Here is a rough outline of the course material:

Introduction: Supervised versus Unsupervised Learning

Unsupervised Learning and Estimation

Distribution Property Testing

Learning Structured Distributions

Method of Moments: Learning Mixture Models

Tensor Methods; Learning Latent Variable Models, Topic Models

Online Learning: Winnow, Perceptron

PAC Learning: Learning Decision Trees and DNFs

Uniform Distribution PAC Learning: Fourier Analysis, Low Degree Algorithm

Learning with Noise and Statistical Queries, Learning Juntas and Noisy Parity

Agnostic Learning, Noise Sensitivity

Learning from Limited Information, Chow Parameters Problem

Lectures

Lecture 1 (January 13) Introduction. Supervised versus Unsupervised Learning. Examples: Learning Linear Separators, Learning Discrete Distributions. Introduction to Property Testing: Testing Uniformity.

Lecture 2 (January 20) Distribution Property Testing: L2 testing, Reduction of L1 testing to L2 testing; Testing Identity, Closeness, and Independence. slides

Lecture 3 (January 27) Analysis of L2 tester; Sample complexity lower bounds via information theory.

Lecture 4 (February 3) Tight Lower Bound for Testing Closeness; Introduction to Learning Structured Distributions. slides

Lecture 5 (February 10) Learning Structured Distributions: Overview of Piecewise Polynomial Learning and Learning Sums of Random Variables. slides

Lecture 6 (February 17) Distribution Learning via Piecewise Polynomial Approximation. slides

Course Evaluation

Homework Assignments: There will be 2 homework assignments will count for 30% of the grade. The assignments which will be proof-based, and are intended to be challenging. Collaboration and discussion among students is allowed, though students must write up their solutions independently.

First Homework: [pdf] (due on March 2)

Course Project: A major part of the course (50% of the grade) is a research project on a topic related to algorithmic aspects of learning theory. Projects can be completed individually or in groups of two students.

The goal of the project is to become an expert in an area related to the class material, and potentially contribute to the state of the art. There are two aspects to the course project. The first is a literature review: Students must decide on a topic and a list of papers, understand these papers in depth, and write a survey presentation of the results in their own words. The second aspect is to identify a research problem/direction on the chosen topic, think about it, and describe the progress they make.

Students must consult with the instructor during the first half of the course for help in forming project teams, selecting a suitable project topic, and selecting a suitable set of research papers. Students will be graded on the project proposal (10%), the progress report (10%), and the final report (20%). Each student will give a project presentation (10%) during the last week of classes.

The remaining part of the grade will be based on class participation (10%) and scribing lecture notes (10%).

Possible project topics can be found here.

Readings

Distribution Property Testing:

Survey article by Rubinfeld; and Section 3 of survey by Canonne.
Two papers: Chan, Diakonikolas, Valiant, and Valiant [pdf]; Diakonikolas and Kane [pdf]
Basics of Information Theory: Chapter 2 of Cover and Thomas book.
Sample Complexity Lower Bounds: Sections 2.3, 2.4, 4.2, 4.3 of Bar-Yossef's thesis; Section 3 of [pdf].

Learning Structured Distributions:

Survey article by instructor.
Two papers: [pdf]; and [pdf]
Useful Probabilistic Tools in Density Estimation: Chapters 3-5 of Devroye-Lugosi book.
Sample Complexity Lower Bounds: Chapter 2 of Tsybakov's book.

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Support Systems

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