Workshop on Computational Mathematics and Data Science

 

 

Time: 22.-24.8.2018
Place: Linnanmaa Campus, Room TS101 (map)

Target group: The course is open for all doctoral candidates, especially in the fields of Mathematics, Statistics, ICT Technology, Natural Sciences and Engineering.

Size: 1-3 credits

Course description

The aim of the course is to teach modern data-centric engineering techniques with solid mathematical basis, a feature which is often missing in deep learning algorithms. The presented latest methods in computational mathematics and data science allow the PhD students to learn and develop further the state-of-the-art techniques and apply them to real-world problems. The course will concentrate both on cutting-edge methods and in applying them in real-world applications, thus allowing interdisciplinary solutions for practical problems. This course covers modern data science techniques, including data assimilation, inverse problems, stochastic deep learning and MCMC techniques.The fields covered include, but are not limited to, applied mathematics, computational statistics, machine learning and computational physics.

Assessment: The course consists of obligatory lectures and study diary or course work. The student will earn 1-3 credits depending on the scope and length of the work. The grade will be pass/fail.

The program of the course: The lecturers are four international experts on Computational Mathematics and Data Science.

Matt Dunlop  has previously worked in Caltech and is  currently postdoctoral research scientist at the Department of Mathematics and Statistics at the University of Helsinki specialised in Bayesian inverse problems, and their applications in machine learning and imaging. Dunlop's work is focused on the development tractable algorithms for sampling with non-Gaussian priors in high dimensions, and applications of function-space methodology to machine learning problems.

Tapio Helin is postdoctoral research scientist at the Department of Mathematics and Statistics at the University of Helsinki specialised in inverse problems related to Bayesian inference. Helin's work is well-balanced between theory and practice, focusing especially on development of the next-generation telescope imaging. Highlights of his work include asymptotics of high-dimensional MAP-estimates.

Tim Sullivan is Junior Professor in Applied Mathematics with Specialism in Risk and Uncertainty Quantification at the Free University of Berlin and Research Group Leader for Uncertainty Quantification at the Zuse Institute Berlin. His work spans numerical analysis, applied probability and statistics, and scientific computation.

Simo Särkkä is Associate Professor in Sensor informatics and medical technology at Aalto University. His research focuses on multi-sensor data processing systems with applications in location sensing, health and medical technology, machine learning, inverse problems, and brain imaging.

Tutorials:

  • Matt Dunlop Gaussian and Deep Gaussian Processes for inference

    • A key decision in the implementation of Bayesian methodology is the choice of prior probability distribution. Gaussian Processes (GPs) are common choices in many applications since their properties are well understood, they are relatively flexible, and they allow for the use of a number of tractable algorithms in high dimensions. Sometimes additionally flexibility is desired however, whilst retaining some of the theoretical and computational advantages of GPs. Deep Gaussian Processes (DGPs) are one approach to this. They are obtained from GPs analogously to how deep neural networks are obtained from shallow neural networks: by iterative composition of layers. These lectures will introduce GPs and DGPs, their key properties, and their implementation for large/high-dimensional inverse problems.

  • Tapio Helin

    • The Bayesian approach to inverse problems is attractive as it provides direct means to quantify uncertainty in the solution. Increases in computational resources have made the Bayesian approach more and more feasible in various large-scale inverse problems, and the approach has gained wide attention in recent years. Due to the computational effort required by Markov chain Monte Carlo algorithms in large-scale problems, there has been interest to study how approximate Bayesian methods can be used effectively in inverse problems. A central estimator used in this research effort is the maximum a posteriori (MAP) estimate. In these lectures, I discuss the non-parametric theory of the MAP estimator in inverse problems and consider related aspects such as differentiability of measures

  • Tim Sullivan Well-posedness of Bayesian inverse problems in function spaces

    • The basic formalism of the Bayesian method is easily stated, and appears in every introductory probability and statistics course:  the posterior probability is proportional to the prior probability times the likelihood.  However, for inference problems in high or even infinite dimension, the Bayesian formula must be carefully formulated and its stability properties mathematically analysed. The paradigm advocated by Andrew Stuart and collaborators since 2010 is that one should study the infinite-dimensional Bayesian inverse problem directly and delay discretisation until the last moment.  These lectures will study the role of various choices of prior distribution and likelihood and how they lead to well-posed or ill-posed Bayesian inverse problems.  If time permits, we will also consider the implications for algorithms, and how Bayesian posterior are summarised (e.g. by maximum a posteriori estimators).
  • Simo Särkkä Bayesian inference in dynamic setting

    • Although Bayesian inference in dynamic setting is, in principle, just a special case of more general Bayesian inference problems, the temporal structure often allows for development of special algorithms for dynamic problems. A particularly fruitful framework for this purpose is that of Bayesian filtering and smoothing, which is also known as recursive Bayesian estimation and can also be seen as the theory behind many data assimilation and dynamic inverse problems solution methods. This series of lectures introduces the current state-of-the-art in the field. The attendees learn what linear and non-linear Kalman filters as well as particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods as well as machine learning methods can be combined with state-of-the-art filtering and smoothing algorithms. The lectures are based on a book by the speaker ("Simo Särkkä (2013). Bayesian Filtering and Smoothing. Cambridge University Press"), which is available from Cambridge University Press (http://www.cambridge.org/sarkka), but is also freely available online in PDF form on author’s web page (https://users.aalto.fi/~ssarkka).
Timetable August 22-24
Wed Thu Fri
9:10-9:15
Opening
   
9:15-10:00
Tim Sullivan
9:15-10:00
Simo Särkkä
9:15-10:00
Simo Särkkä
10:15-11:00
Tim Sullivan
10:15-11:00
Simo Särkkä
10:15-11:00
Simo Särkkä
11:00-13:00
Lunch break
11:00-13:00
Lunch break
11:00-13:00
Lunch break
13:00-13:45
Matt Dunlop
13:00-13:45
Matt Dunlop
13:00-13:45
Matt Dunlop
13:45-14:15
Coffee
13:45-14:15
Coffee
13:45-14:15
Coffee
14:15-15:00
Matt Dunlop
14:15-15:00
Tapio Helin
14:15-15:00
Tapio Helin
15:00-15:45
Tapio Helin
15:00-15:45
Tim Sullivan
15:00-15:45
Tapio Helin

 

Registrations

Registrations in the course using the web-form in this link.

Organizer

Technology and Natural Sciences Doctoral Programme in collaboration with Department of Mathematical Sciences of the University of Oulu, Sodankylä Geophysical Observatory and Aalto University.

Further information

  • Practical issues Sari Lasanen (sari.lasanen at oulu.fi )
  • Scientific issues Lassi Roininen (lassi.roininen at oulu.fi)

Last updated: 20.8.2018