SCCS Colloquium - Aug 26, 2020

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Date: Aug 19, 2020
Room: Online (password: 075537) - Different link this time!
Time: 10:00-11:00 (only this time)

Lukas Schulte: Sparse Grid Density Estimation with the Combination Technique

Bachelor's thesis submission talk. Lukas is advised by Michael Obersteiner and Paul Sarbu.

In the frame of this bachelor thesis, density estimation with the sparse grid combination technique was implemented and integrated into the sparseSpACE framework. The sparse grid combination technique is used to compute a sparse grid, whereby a specific sequence of small anisotropic full grids is combined linearly, to tackle the curse of dimensionality. The usage of mass lumping in the density estimation process is also explored, which still achieves relatively good results compared to the standard combination method. The density function is estimated for different data sets using the combination technique and compared with the full grid solution in regards to different error norms. The test results show that we achieve a good estimate of the density function while simultaneously reducing the number of grid points used.

Keywords: density estimation, sparse grids, sparseSpACE, combination technique

Alexandre Mercier: Study of Density Difference and Density Ratio Estimation using Sparse Grids

Bachelor's thesis submission talk. Alexandre is advised by Paul Sarbu.

Using sparse grids for density estimation can reduce computational expenses in comparison to more popular kernel density methods by reducing the amount of examined points, especially for datasets in higher dimensions. The goal of this thesis is to study two recently added algorithms for density difference and density ratio estimation in the SG++ code library for sparse grids. Using a custom pipeline, experiments studying the behavior and accuracy of the algorithms can be compared to the analytical solution and kernel based density estimation methods. We aim to visualize and quantify the differences between sparse grid based solutions and other solutions to demonstrate their accuracy and usability for future use in high-dimensional applications and time-series segmentation.

Keywords: Sparse grid SG++ python density difference ratio estimation