1. komponenta

Lecture type	Total
Lectures	30
Exercises	15

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE OBJECTIVES:
After having completed the course, students should be able to:
1. Formulate a data analytics problem as an optimisation problem
2. Estimate the requirements of the underlying dataset size
3. Implement the appropriate optimisation algorithm
4. Decide on the appropriate stopping criterion to obtain the meaningful accuracy of the learning task

COURSE CONTENT:
1. Basics of data modelling (regression, classification, clustering).
2. Introduction to statistical justification of data analytics (empirical risk minimisation).
3. Review of convex analysis (separation theorems, gradient descent methods, duality theory, optimisation of separable, pairwise separable and composite convex functions).
4. Regression and classification methods. Least square and least absolute deviation method. Generalised linear models, neural networks, support vector machines, least absolute shrinkage and selection operator.
5. Methods for reconstructing and segmenting images (singular value decomposition for matrices and tensors, regularisation and optimisation).
6. Scaling methods to large datasets.
7. Validation of the fitted model.

1. Statistics for High-Dimensional Data. Methods, Theory and Applications, Bühlmann, Peter, van de Geer, Sara, Springer.
2. Computational Statistics, Peter Buehlmann and Martin Maechler, ETH Zuerich, 2008.
3. Convex Optimization, Stephen Boyd and Lieven Vandenberghe, Cambridge University Press.
4. Mathematics of Data: From Theory to Computation, Volkan Cevher, EPFL course materials.
5. The course will include guest lectures on various applications of optimisation for modelling in a data rich environment.

Mandatory course - Regular study - Biomedical Mathematics