Nonlinear Statistics
Provider: Faculty of Science

Activity no.: 5166-17-02-31 
Enrollment deadline: 31/05/2017
PlaceBiocenteret, Room 4-0-02
Ole Maaløes Vej 5, 2200 København N
Date and time12.06.2017, at: 09:00 - 16.06.2017, at: 16:00
Regular seats46
ECTS credits2.50
Contact personAasa Feragen    E-mail address:
Enrolment Handling/Course OrganiserStefan Horst Sommer    E-mail address:
Written languageEnglish
Teaching languageEnglish
Course workload
Course workload categoryHours
Preparation / Self-Study10.00
Course hours40.00
Evaluation / reporting15.00


Subject area:

Nonlinear statistics is an increasingly active research field at the intersection of geometry, statistics, machine learning and algorithmics. Nonlinear statistics seeks to answer fundamental questions that arise when defining new statistical models and tools for analysis of data that exhibits nonlinearity. Such data is becoming increasingly prevalent in diverse fields including computational anatomy, phylogenetics, and computational biology, and are also receiving increased interest in machine learning, where nonlinearity adds to the possible flexibility of a predictive model. In addition to impact on applied problems, theoretical advances in nonlinear statistics also provides new insight into methodology from traditional linear statistics.

Scientific content:

The course will consist of 5 days with lectures before lunch and exercise sessions after lunch. In addition, students will be expected to read a pre-defined set of scientific articles on nonlinear statistics prior to the course, and write a report on nonlinear statistics and its potential use in their own research field after the course. The course will consist of three modules corresponding to the three external lecturers,

o Models and numerical solutions for manifold statistics (Tom Fletcher, Stefan Sommer)
o Models and numerical solutions for statistics in non-smooth spaces (Tom Nye, Aasa Feragen)
o Elastic metrics for shape analysis (Anuj Srivastava)

The first module will introduce standard methods in manifold statistics and recent advances on these. Manifolds are the most commonly used nonlinear data spaces, and also the most tractable computationally.

The second module will introduce methods available in nonlinear data spaces that are not manifolds – in other words, they are not smooth. This is relevant for structured data such as trees and graphs, as well as data with degeneracies such as diffusion tensors or non-diffeomorphic registration deformations.

The third module will introduce the elastic shape analysis framework developed by A. Srivastava, which has proven useful in a wide range of applications.

Learning outcome
After participating in this course, the student should:

- Have a strong knowledge of basic concepts in nonlinear statistics (geodesic-based statistics such as Fréchet means and geodesic PCA; diffusion-based statistics)
- Be able to implement basic numerical tools for statistics on nonlinear data spaces
- Have experience working with several types of data residing in nonlinear data spaces (covariance matrices, trees, shapes)
- Be aware of current open problems and developments in nonlinear statistics

Guest lecturers:

Professor Anuj Srivastava, Department of Statistics, Florida State University (tentatively confirmed).

Tom Nye, Senior Lecturer in Statistics, Newcastle University (tentatively confirmed).

Tom Fletcher, Associate Professor, Scientific Computing and Imaging institute, University of Utah.

Teachers from UCPH-SCIENCE:

Assistant professor Stefan Sommer (
Associate professor Aasa Feragen (

Course website:

No-show fee:
100% absence from the course will be charged with a fee of 50 EUR
no-show for the conference dinner will be charged with a fee of 50 EUR