Target audience

Master's students in computer science (specialization in algorithms & machine learning, or bioinformatics), applied mathematics (specialization statistical machine learning or e.g. stochastics), or statistics.

Description

Unsupervised learning is one of the main streams of machine learning, and closely related to exploratory data analysis and data mining. This course describes some of the main methods in unsupervised learning.

In recent years, machine learning has become heavily dependent on statistical theory which is why this course is somewhere on the borderline between statistics and computer science. Emphasis is put both on the statistical formulation of the methods as well as on their computational implementation. The goal is not only to introduce the methods on a theoretical level but also to show how they can be implemented in scientific computing environments such as Matlab or R.

Computer projects are an important part of the course, but they are given separate credits, see Projects for Unsupervised Machine Learning. The projects will be given in the exercice session marked below in the schedule.

One of the weekly sessions (usually Friday) will be an exercice session, the possibly final timetable is as follows (note Easter break in the last line): 

The exercices will be taught by Jouni Puuronen and the computer projects by Hugo Eyherabide.

Prerequisites

• Computer science majors: Bachelor's degree recommended. It should include the following mathematics courses: calculus (including vector calculus), linear algebra I&II, introduction to probability. You should also have done "Introduction to machine learning" in Period II.
• Statistics majors: Bachelor's degree recommended.
• Mathematics majors: Bachelor's degree recommended. It should include basic courses in calculus (including vector calculus), linear algebra I&II, introduction to probability, introduction to statistical inference.

Contents

• Introduction. Supervised vs. unsupervised learning. Applications of unsupervised learning. Probabilistic formulation. Review of some basic mathematics (linear algebra, probability)
• Numerical optimization. Gradient method, Newton's method, stochastic gradient, projected gradient methods
• Principal component analysis and factor analysis. Formulation as minimization of reconstruction error or maximization of component variance. Computation using covariance matrix and its eigen-value decomposition. Factor analysis and interpretation of PCA as estimation of gaussian generative model. Factor rotations.
• Independent component analysis. Problem of blind source separation, why non-gaussianity is needed for identifiability. Correlation vs. independence. ICA as maximization of non-gaussianity, measurement of non-Gaussianity by cumulants. Likelihood of the model and maximum likelihood estimation. Implementation by gradient methods and FastICA. Applications of component analysis.
• Clustering. K-means algorithm.Gaussian mixture model: Maximization of likelihood, EM algorithm.
• Nonlinear dimension reduction. Non-metric multi-dimensional scaling and related methods: kernel PCA, Laplacian eigenmaps, IsoMap. Kohonen's self-organizing map