SC²S Colloquium - September 14, 2016
|Date:||September 14, 2016|
|Time:||3:00 pm, s.t.|
Thomas Hain: Performance analysis of the Chaospy Framework
This thesis aims at measuring the Chaospy framework’s performance in the context of scientific calculations. Therefore, it evaluates and analyses its memory efficiency as well as the required execution time per function. For this cause a test model of the 1D Burger’s Equation was developed based on the finite difference scheme. After that, the analysis and evaluation proposals are presented, which lead to improvements in Chaospy’s general performance. This opens up the possibility of solving even higher scale problems.
Lukas Krenz: Integration of Prior Knowledge for Regression and Classification with Sparse Grids
This thesis discusses different ways of imposing prior knowledge about datasets on the sparse grid model for supervised learning. We introduce a Tikhonov regularization method that uses information about the smoothness of the function we want to approximate. We also present the sparsity-inducing penalties lasso, elastic net, and group lasso. The different regularization approaches are compared with the standard ridge regularization. Because some regularization penalties are not differentiable, we discuss the fast iterative shrinkage-thresholding algorithm and show how it can be used in conjunction with our added regularization methods. Furthermore, we modify the grid generation procedure. The first discussed method is generalized sparse grids, which allows us to control the granularity of the grid. The second method is interaction-term aware sparse grids, which are used to construct smaller and more efficient grids for image recognition problems. All methods were implemented with the SG++ library and showed promising results for both artificial and real-world datasets.