FINM 33180 1 (Autumn 2021) Multivariate Data Analysis via Matrix Decompositions
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.