Seminar Machine Learning

Content

Time. Tuesdays 13.15-15.00.

Interested in participating? In case you would like to participate in the seminar, please send an email to Sjoerd Dirksen (s.dirksen@uu.nl) with a brief description of your background and possible topics that you would be interested in. There is a maximum of 12 (active) participants.

Topic. The topic of this seminar is machine learning, a field of science that designs methods to automatically detect patterns in data and make predictions based on them, without providing a computer with explicit instructions on how to accomplish a given task. There is a long list of problems where machine learning has proven successful, including spam filtering, fraud detection, image recognition, and speech recognition. Machine learning is a rich and very active area, with strong influences from optimization theory, probability, statistics, and functional analysis.

The goal of this seminar is to give an introduction to the mathematical theory of machine learning. We will discuss fundamental concepts of statistical learning, as well as a selection of successful machine learning algorithms.

Content. The content of the seminar will be fixed based on the interest and background of the participants. Possible directions include:

• Support vector machines
• Kernel methods
• Boosting
• Neural networks
• Random forests
• Clustering
• Dimensionality reduction

The organizer will provide a list of presentation topics before the start of the seminar. Participants are also welcome to suggest additional topics. Examples of additional topics treated in the past are reinforcement learning, topic modelling with Latent Dirichlet Allocation, mixture density networks, agent-based modelling, and recurrent neural networks.

We will fix a schedule at the first meeting, based on the participants’ backgrounds and preferences. Participants with prior knowledge of machine learning (e.g., acquired through the introductory bachelor course WISB365) are expected to present more advanced topics.

Material. Material for the seminar is drawn from the following textbooks:

• Ian Goodfellow, Yoshua Bengio, and Aaron Courville, Deep learning, MIT Press, 2016
• Mehryar Mohri, Afshin Rostamizadeh and Ameet Talwalkar, Foundations of Machine Learning, MIT Press, 2012
• Shai Shalev-Shwartz and Shai Ben-David, Understanding Machine Learning: from Theory to Algorithms, Cambridge University Press, 2014
• Trevor Hastie, Robert Tibshirani, and Jerome Friedman, The Elements of Statistical Learning, Springer, 2009

Depending on the interest of the participants, additional recent research papers may be provided.

Prerequisites. Understanding of basic analysis, linear algebra and probability theory. Some topics require prior knowledge of continuous optimization theory or functional analysis. Prior knowledge of machine learning is not required.

Format. There is a maximal number of 12 (active) participants. All participants are expected to give a seminar talk (with a duration of 2 x 45 minutes), possibly more or less depending on the number of participants. They will write a handout for their fellow participants before their presentation. They will pose a hand-in assignment to the other seminar participants (to be handed in at the next lecture), that needs to be approved beforehand by the seminar organizer. The speaker is responsible for grading this hand-in assignment. In case of discussion about the solutions or the grading, the seminar organizer makes the final decision. It is obligatory to be present at all talks in this seminar (unless there are exceptional circumstances).

Evaluation. The final grade for the seminar is composed as follows:

• effective communication of the material during presentation (30%)
• quality of handout and assignment and correction of assignment (40%)
• homework grades (30%)

Learning goals. After completion of the course, the student is able to:

• convert material from part of a graduate-level textbook or a scientific paper into a coherent and comprehensible presentation for fellow students and mathematicians in general
• choose appropriate means of communicating mathematics to fellow students and mathematicians, both in written and oral form
• formulate and correct exercises that keep a balance between relevance, interest, and feasibility
• explain specific topics from the content list of the seminar to fellow students, and put them in perspective as far as their relevance to wider mathematics is concerned