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Matrix Computations in Statistics with Applications

General aims of the course

The aim of the course is to enable students to understand and use important techniques in Computational Statistics. The students will study computational methods used in Statistics with emphasis on large-scale computations and will develop understanding and skills how to use these appropriately in research and applications. The importance of how to efficiently implement those methods on the available parallel and high performance computer (HPC) facilities will be emphasized too.

Content

Regression analysis: Statistical concepts, Multiple regression. Polynomial regression. General linear model and linear models with sparse data matrices. Least Squares,  QR factorization, singular value decomposition (SVD). Normal equations vs QR factorization. Computing the SVD. Principal Component Analysis. Eigenvalue computations (large scale, sparse, loss of orthogonality). Partial Least Squares. Graphs and their usage in Statistical applications (page-rank), regression trees and classification trees. Concepts of numerical stability. Solving Least Squares problems with sparse matrices: direct and iterative methods (Krylov methods, Partial Least Squares).

Course Schedule

  •       Preparation, self-reading: March 14-18
  •       Lectures in Uppsala: March 21-25
  •       Project work: March 28 – April 1

Please note, that since 25.3 is a day off, it will be free of teaching,
however the time for lectures and labs during 21.3 to 14.3 will be longer.

Detailed Schedule

Detailed schedule for 2016 t.b.a.

The detailed schedule for 2014

Prerequisites

The course requires basic knowledge of  statistics, linear algebra and numerical linear algebra. Some experience with R or MATLAB is necessary.

Course Literature

  1. Lars Eldén. Matrix Methods in Data Mining and Pattern Recognition.
    SIAM, Philadelphia, PA, USA, 2007.
  2. James E. Gentle, Computational Statistics, Springer, 2009.

Lecturers

  • Lars Eldén
  • Maya Neytcheva
  • Dietrich von Rosen

Contact

Maya Neytcheva maya.neytcheva at it.uu.se