Workshop on Computational Mathematics and Data Science

Time: 22.-24.8.2018
Place: Linnanmaa Campus

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.

Sergios Agapiou is a lecturer of Statistics and Probability  at the Department of Mathematics and Statistics at University of Cyprus. His expertise is in the area of Bayesian nonparametric statistics, with a focus on the asymptotic performance of posterior distributions, Bayesian inverse problems and the analysis of Monte Carlo algorithms.  

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:

  • Sergios Agapiou: Rates of contraction of posterior distributions with product priors: beyond Gaussianity
    • We will study the asymptotic performance of posterior distributions arising in nonparametric settings, in the infinitely informative limit. In particular, we will consider a frequentist setup in which the observations are generated from a fixed underlying true value of the unknown parameter, and will study rates of contraction of the posterior distribution around the truth. We will start by reviewing the general posterior contraction theory of Subhashis Ghosal and Aad van der Vaart, as well as the general contraction results for Gaussian priors due to Aad van der Vaart and Harry van Zanten. We will then introduce the class of p-exponential priors, study some of their properties and prove general posterior contraction results for p-exponential priors. Finally, we will study the white noise model with p-exponential priors and will use our general results to obtain (minimax) optimal rates of posterior contraction in the small noise limit.
  • Tapio Helin:TBD
  • 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:TBD
Timetable August 22-24
Wed Thu Fri
9:10-9:15
Opening
   
9:15-10:00
Tapio Helin
9:15-10:00
Simo Särkkä
9:15-10:00
Tapio Helin
10:15-11:00
Tim Sullivan
10:15-11:00
Simo Särkkä
10:15-11:00
Tapio Helin
11:00-13:00
Lunch break
11:00-13:00
Lunch break
11:00-13:00
Lunch break
13:00-13:45
Sergios Agapiou
13:00-13:45
Sergios Agapiou
13:00-13:45
Simo Särkkä
13:45-14:15
Coffee
13:45-14:15
Coffee
13:45-14:15
Coffee
14:15-15:00
Sergios Agapiou
14:15-15:00
Tim Sullivan
14:15-15:00
Sergios Agapiou
15:00-15:45
Tapio Helin
15:00-15:45
Tim Sullivan
15:00-15:45
Simo Särkkä

 

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: 30.6.2018