Search result: Catalogue data in Spring Semester 2021

Mathematics Bachelor Information
Electives
Selection: Further Realms
NumberTitleTypeECTSHoursLecturers
401-2684-00LMathematics of Machine Learning Information W5 credits2V + 1UA. Bandeira, N. Zhivotovskii
AbstractIntroductory course to Mathematical aspects of Machine Learning, including Supervised Learning, Unsupervised Learning, Sparsity, and Online Learning.
ObjectiveIntroduction to Mathematical aspects of Machine Learning.
ContentMathematical aspects of Supervised Learning, Unsupervised Learning, Sparsity, and Online Learning. This course is a Mathematical course, with Theorems and Proofs.
Prerequisites / NoticeNote for non Mathematics students: this class requires a certain degree of mathematical maturity--including abstract thinking and the ability to understand and write proofs.
401-4944-20LMathematics of Data Science
Does not take place this semester.
W8 credits4GA. Bandeira
AbstractMostly self-contained, but fast-paced, introductory masters level course on various theoretical aspects of algorithms that aim to extract information from data.
ObjectiveIntroduction to various mathematical aspects of Data Science.
ContentThese topics lie in overlaps of (Applied) Mathematics with: Computer Science, Electrical Engineering, Statistics, and/or Operations Research. Each lecture will feature a couple of Mathematical Open Problem(s) related to Data Science. The main mathematical tools used will be Probability and Linear Algebra, and a basic familiarity with these subjects is required. There will also be some (although knowledge of these tools is not assumed) Graph Theory, Representation Theory, Applied Harmonic Analysis, among others. The topics treated will include Dimension reduction, Manifold learning, Sparse recovery, Random Matrices, Approximation Algorithms, Community detection in graphs, and several others.
Lecture notesLink
Prerequisites / NoticeThe main mathematical tools used will be Probability, Linear Algebra (and real analysis), and a working knowledge of these subjects is required. In addition
to these prerequisites, this class requires a certain degree of mathematical maturity--including abstract thinking and the ability to understand and write proofs.


We encourage students who are interested in mathematical data science to take both this course and ``227-0434-10L Mathematics of Information'' taught by Prof. H. Bölcskei. The two courses are designed to be
complementary.
A. Bandeira and H. Bölcskei
252-0220-00LIntroduction to Machine Learning Information Restricted registration - show details
Limited number of participants. Preference is given to students in programmes in which the course is being offered. All other students will be waitlisted. Please do not contact Prof. Krause for any questions in this regard. If necessary, please contact Link
W8 credits4V + 2U + 1AA. Krause, F. Yang
AbstractThe course introduces the foundations of learning and making predictions based on data.
ObjectiveThe course will introduce the foundations of learning and making predictions from data. We will study basic concepts such as trading goodness of fit and model complexitiy. We will discuss important machine learning algorithms used in practice, and provide hands-on experience in a course project.
Content- Linear regression (overfitting, cross-validation/bootstrap, model selection, regularization, [stochastic] gradient descent)
- Linear classification: Logistic regression (feature selection, sparsity, multi-class)
- Kernels and the kernel trick (Properties of kernels; applications to linear and logistic regression); k-nearest neighbor
- Neural networks (backpropagation, regularization, convolutional neural networks)
- Unsupervised learning (k-means, PCA, neural network autoencoders)
- The statistical perspective (regularization as prior; loss as likelihood; learning as MAP inference)
- Statistical decision theory (decision making based on statistical models and utility functions)
- Discriminative vs. generative modeling (benefits and challenges in modeling joint vy. conditional distributions)
- Bayes' classifiers (Naive Bayes, Gaussian Bayes; MLE)
- Bayesian approaches to unsupervised learning (Gaussian mixtures, EM)
LiteratureTextbook: Kevin Murphy, Machine Learning: A Probabilistic Perspective, MIT Press
Prerequisites / NoticeDesigned to provide a basis for following courses:
- Advanced Machine Learning
- Deep Learning
- Probabilistic Artificial Intelligence
- Seminar "Advanced Topics in Machine Learning"
263-5300-00LGuarantees for Machine Learning Information Restricted registration - show details
Number of participants limited to 30.

Last cancellation/deregistration date for this graded semester performance: 17 March 2021! Please note that after that date no deregistration will be accepted and a "no show" will appear on your transcript.
W7 credits3G + 3AF. Yang
AbstractThis course is aimed at advanced master and doctorate students who want to conduct independent research on theory for modern machine learning (ML). It teaches classical and recent methods in statistical learning theory commonly used to prove theoretical guarantees for ML algorithms. The knowledge is then applied in independent project work that focuses on understanding modern ML phenomena.
ObjectiveLearning objectives:

- acquire enough mathematical background to understand a good fraction of theory papers published in the typical ML venues. For this purpose, students will learn common mathematical techniques from statistics and optimization in the first part of the course and apply this knowledge in the project work
- critically examine recently published work in terms of relevance and determine impactful (novel) research problems. This will be an integral part of the project work and involves experimental as well as theoretical questions
- find and outline an approach (some subproblem) to prove a conjectured theorem. This will be practiced in lectures / exercise and homeworks and potentially in the final project.
- effectively communicate and present the problem motivation, new insights and results to a technical audience. This will be primarily learned via the final presentation and report as well as during peer-grading of peer talks.
ContentThis course touches upon foundational methods in statistical learning theory aimed at proving theoretical guarantees for machine learning algorithms, touching on the following topics
- concentration bounds
- uniform convergence and empirical process theory
- high-dimensional statistics (e.g. sparsity)
- regularization for non-parametric statistics (e.g. in RKHS, neural networks)
- implicit regularization via gradient descent (e.g. margins, early stopping)
- minimax lower bounds

The project work focuses on current theoretical ML research that aims to understand modern phenomena in machine learning, including but not limited to
- how overparameterization could help generalization ( RKHS, NN )
- how overparameterization could help optimization ( non-convex optimization, loss landscape )
- complexity measures and approximation theoretic properties of randomly initialized and trained NN
- generalization of robust learning ( adversarial robustness, standard and robust error tradeoff, distribution shift)
Prerequisites / NoticeIt’s absolutely necessary for students to have a strong mathematical background (basic real analysis, probability theory, linear algebra) and good knowledge of core concepts in machine learning taught in courses such as “Introduction to Machine Learning”, “Regression”/ “Statistical Modelling”. In addition to these prerequisites, this class requires a high degree of mathematical maturity—including abstract thinking and the ability to understand and write proofs.

Students have usually taken a subset of Fundamentals of Mathematical Statistics, Probabilistic AI, Neural Network Theory, Optimization for Data Science, Advanced ML, Statistical Learning Theory, Probability Theory (D-MATH)
227-0432-00LLearning, Classification and Compression Information W4 credits2V + 1UE. Riegler
AbstractThe focus of the course is aligned to a theoretical approach of learning theory and classification and an introduction to lossy and lossless compression for general sets and measures. We will mainly focus on a probabilistic approach, where an underlying distribution must be learned/compressed. The concepts acquired in the course are of broad and general interest in data sciences.
ObjectiveAfter attending this lecture and participating in the exercise sessions, students will have acquired a working knowledge of learning theory, classification, and compression.
Content1. Learning Theory
(a) Framework of Learning
(b) Hypothesis Spaces and Target Functions
(c) Reproducing Kernel Hilbert Spaces
(d) Bias-Variance Tradeoff
(e) Estimation of Sample and Approximation Error

2. Classification
(a) Binary Classifier
(b) Support Vector Machines (separable case)
(c) Support Vector Machines (nonseparable case)
(d) Kernel Trick

3. Lossy and Lossless Compression
(a) Basics of Compression
(b) Compressed Sensing for General Sets and Measures
(c) Quantization and Rate Distortion Theory for General Sets and Measures
Lecture notesDetailed lecture notes will be provided.
Prerequisites / NoticeThis course is aimed at students with a solid background in measure theory and linear algebra and basic knowledge in functional analysis.
401-3502-21LReading Course Restricted registration - show details
To start an individual reading course, contact an authorised supervisor
Link
and register your reading course in myStudies.
W2 credits4ASupervisors
AbstractFor this Reading Course proactive students make an individual agreement with a lecturer to acquire knowledge through independent literature study.
Objective
401-3503-21LReading Course Restricted registration - show details
To start an individual reading course, contact an authorised supervisor
Link
and register your reading course in myStudies.
W3 credits6ASupervisors
AbstractFor this Reading Course proactive students make an individual agreement with a lecturer to acquire knowledge through independent literature study.
Objective
401-3504-21LReading Course Restricted registration - show details
To start an individual reading course, contact an authorised supervisor
Link
and register your reading course in myStudies.
W4 credits9ASupervisors
AbstractFor this Reading Course proactive students make an individual agreement with a lecturer to acquire knowledge through independent literature study.
Objective
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