Foundations of Data Analysis
Instructor : Jeff Phillips (email) | Office hours: Thursdays 10am @ MEB 3442 (and directly after class in WEB 2230)
TAs: Benwei Shi (email) | Office hours: Tuesdays and Thursdays 2-3pm in MEB 3423.
         Alok Jadhav (email) | Office hours: Mondays 1-3pm in MEB 3423.
Fall 2019 | Mondays, Wednesdays 3:00 pm - 4:20 pm
WEB 2230
Catalog number: CS 3190 01

This class will be an introduction to computational data analysis, focusing on the mathematical foundations. The goal will be to carefully develop and explore several core topics that form the backbone of modern data analysis topics, including Machine Learning, Data Mining, Artificial Intelligence, and Visualization. This will include some background in probability and linear algebra, and then various topics including Bayes Rule and its connection to inference, linear regression and its polynomial and high dimensional extensions, principal component analysis and dimensionality reduction, as well as classification and clustering. We will also focus on modern PAC (probably approximately correct) and cross-validation models for algorithm evaluation.
These topics are often very breifly covered at the end of a probability or linear algebra class, and then are often assumed knowledge in advanced data mining or machine learning classes. This class will fill that gap. The planned pace will be closer to CS3130 or Math2270 than the 5000-level advanced data analysis courses.

We will use Python in the class to demonstrate and explore basic concepts. But programming will not be the main focus.

Book: Mathematical Foundations of Data Analysis (v5.0)
This is a draft of a book I started writing in Fall 2016 for this course.
More outside online resources are listed below.

Videos: We will plan to live stream and post videos for each lecture on a YouTube playlist. The quality is not perfect, but probably good enough in case you miss the occaisional lecture.

The official pre-requisites are CS 2100, CS 2420, and Math 2270. These are to ensure a certain very basic mathematical maturity (CS 2100) a basic understanding of how to store and manipulate data with some efficiency (CS2420), and basics of linear algebra and high dimensions (MATH 2270).
We have as a co-requisite CS 3130 (or Math 3070) to ensure some familiarity with probability.
A few lectures will be devoted to review linear algebra and probability, but at a fast pace and a focus on the data interpretation of these domains.
This class will soon become a pre-requisite for CS 5350 (Machine Learning) and CS 5140 (Data Mining), as part of a new Data Science pipeline.

Tenative Schedule:

Date Chapter Topic Assignment
Mon 8.19 Class Overview
Wed 8.21 Ch 1 - 1.2 Probability Review : Sample Space, Random Variables, Independence
Mon 8.26 Ch 1.3 - 1.6 Probability Review : PDFs, CDFs, Expectation, Variance, Joint and Marginal Distributions HW1 out
Wed 8.28 Ch 1.7 Bayes Rule
Mon 9.02
Wed 9.04 Ch 1.8 Bayes Rule : Bayesian Reasoning
Mon 9.09 Ch 2.1 Convergence : Central Limit Theorem and Estimation
Wed 9.11 Ch 2.2 - 2.3 Convergence : PAC Algorithms and Concentration of Measure HW 1 due
Mon 9.16 Ch 3.1 - 3.2 Linear Algebra Review : Vectors, Matrices, Multiplication and Scaling
Quiz 1
Wed 9.18 Ch 3.3 - 3.5 Linear Algebra Review : Norms, Linear Independence, Rank (colab) HW 2 out
Mon 9.23 Ch 3.6 - 3.8 Linear Algebra Review : Inverse, Orthogonality, numpy
Wed 9.25 Ch 5.1 Linear Regression : dependent, independent variables (colab)
Mon 9.30 Ch 5.2-5.3 Linear Regression : multiple regression (colab), polynomial regression (colab) HW 2 due
Wed 10.02 Ch 5 Linear Regression : mini review + slack
Quiz 2
Mon 10.09
Wed 10.11
Mon 10.14 Ch 5.4 Linear Regression : overfitting and cross-validation (colab) HW 3 out
Wed 10.16 Ch 6.1 - 6.2 Gradient Descent : functions, minimum, maximum, convexity & gradients
Mon 10.21 Ch 6.3 Gradient Descent : algorithmic variants (colab)
Wed 10.23 Ch 6.4 Gradient Descent : fitting models to data and stochastic gradient descent
Mon 10.28 Ch 7.1 - 7.2 PCA : SVD (colab)
Wed 10.30 Ch 7.2 - 7.3 PCA : rank-k approximation and eigenvalues HW 3 due
Mon 11.04 Ch 7.4 PCA : power method (colab) HW 4 out
Wed 11.06 Ch 7.5 - 7.6 PCA : centering, MDS, and dimensionalty reduction + (practice quiz)
Mon 11.11 Ch 8.1 Clustering : Voronoi Diagrams
Quiz 3
Wed 11.13 Ch 8.3 Clustering : k-means
Mon 11.18 Ch 8.4, 8.7 Clustering : EM, Mixture of Gaussians, Mean-Shift
Wed 11.20 Ch 9.1 Classification : Linear prediction HW 4 due
Mon 11.25 Ch 9.2 Classification : Perceptron Algorithm HW 5 out
Wed 11.27 Ch 9.3 Classification : Kernels and SVMs
Mon 12.02 Ch 9.4 - 9.5 Classification : Neural Nets
Quiz 4
Wed 12.04 In-class review
Fri 12.06 HW 5 due
Thu 12.12
FINAL EXAM (3:30pm - 5:30pm)

Class Organization: The class will be run through this webpage, and Canvas. The schedule, notes, and links will be maintained here. All homeworks will be turned in through Canvas.

Grading: There will be one final exam with 20% of the grade. Homeworks and quizzes will be worth 80% of the grade. There will be 5 homeworks and 4 quizzes -- the lowest one (either one homework or one quiz) can be dropped. So each counted homework/quiz will be worth 10% of the grade.

The homeworks will usually consist of an analytical problems set, and sometimes light programming exercizes in python. When python will be used, we typically will work through examples in class first.

Late Policy: To get full credit for an assignment, it must be turned in through Canvas by the start of class, specifically 2:45. Once the 2:45 deadline is missed, those turned in late will lose 10%. Every subsequent 24 hours until it is turned another 10% is deducted. That is, a homework 30 hours late worth 10 points will have lost 2 points. Once the graded assignment is returned, or 48 hours has passed, any assignment not yet turned in will be given a 0.

Academic Conduct Policy: The Utah School of Computing has an academic misconduct policy, which requires all registered students to sign an Acknowledgement Form. This form must be signed and turned into the department office before any homeworks are graded.

This class has the following collaboration policy:
For assignments, students may discuss answers with anyone, including problem approach, proofs, and code. But all students must write their own code, proofs, and write-ups. If you collaborated with another student on homeworks to the extent that you expect your answers may start to look similar, you must explain the extent to which you collabodated explicitly on the homework. Students whose homeworks appear too similar, and did not explain the collaboration will get a 0 on that assignment.

For quizzes and the final exam, talking to anyone (other than instructors/TAs) during the examination period is not allowed and will result in a 0 on that test or quiz.

More Resources:
Here are a few books that cover some of the material, but at a more advanced level:
Understanding ML | Foundations of Data Science | Introduction to Statistical Learning
Here is a list nice resources I believe may be useful with relevant parts at roughly the right level for this course:
  • Probability: ProbStat course | P1 | P2
  • Bayes Rule/Reasoning: B1 | B2 | B3 | B4
  • Linear Algebra: No-BS Book | LA1 | LA2 | LA3
  • Linear Regression: LR1 | LR2
  • Gradient Descent: GD1 | GD2
  • PCA: PCA1 | PCA2 | PCA3 | PCA4
  • Clustering: C1 | C2 | C3 | C4
  • Classification: L1 | L2 | L3