# FINM 33180/STAT 32940. Multivariate Data Analysis via Matrix Decompositions

### Department of Statistics University of Chicago Fall 2020

This course is about using matrix computations to infer useful information from observed data. One may view it as an "applied" version of Stat 309; the only prerequisite for this course is basic linear algebra. The data analytic tools that we will study will go beyond linear and multiple regression and often fall under the heading of "Multivariate Analysis" in Statistics or "Unsupervised Learning" in Machine Learning. These include factor analysis, correspondence analysis, principal components analysis, multidimensional scaling, canonical correlation analysis, Procrustes analysis, partial least squares, etc. We would also discuss a small number of supervised learning techniques including discriminant analysis and support vector machines. Understanding these techniques require some facility with matrices (primarily eigen and singular value decompositions, as well as their generalization) in addition to some basic statistics, both of which the student will acquire during the course.

## Announcements

• 09/22/20: This year's class will be conducted entirely on Canvas. This webpage would be used only as a mirror repository for course materials.

## Lectures

Location: Lectures held online through Canvas.

Times: Mon, 6:30–9:30pm

## Course staff

Instructor: Lek-Heng Lim
Office: Jones 122C
lekheng(at)uchicago.edu
Tel: (773) 702-4263
Office hours: Tue 2:00–4:00 pm

Course Assistant I: Jinhong Du
dujinhong(at)uchicago.edu
Office hours: Fri 3:00–5:00 pm.

Course Assistant II: Wenxuan Guo
wxguo(at)uchicago.edu
Office hours: Tue 9:00–11:00 am.

## Syllabus

The last two applications fall under supervised learning but we will discuss them if time permits, if only to give an idea of how supervised learning differs from unsupervised learning.

• Tools:
• EVD = Eigenvalue decomposition
• SVD = Singular value decomposition
• GEVD = Generalized eigenvalue decomposition
• GSVD = Generalized singular value decomposition
• Applications:
• Principal component analysis (SVD)
• Factor analysis (EVD)
• Canonical correlation analysis (EVD)
• Correspondence analysis (GSVD)
• Hyperlink induced topic search (SVD)
• Latent semantic indexing (SVD)
• Procrustes analysis (SVD)
• Multidimensional scaling (EVD)
• Partial least squares (SVD)
• Linear discriminant analysis (GEVD)
• Support vector machines

## Problem Sets

Collaborations are permitted but you will need to write up your own solutions and declare your collaborators. The problem sets are designed to get progressively more difficult. You will get about 10 days for each problem set.

You are required to implement your own programs for problems that require some amount of simple coding (using Matlab, Mathematica, R, or SciPy).

Bug report on the problem sets: lekheng(at)uchicago.edu