Johannes Schade

Bi-invariant Geodesic Regression

The thesis extends Riemannian geodesic Regression (Fletcher 2012) to Lie groups without making use of the Riemannian metric. This is desirable, since for many Lie groups, bi-invariant metrics do not exist. The thesis will not only study mathematical properties of such a proposal, but also experiment with synthetic and medical image data to test this on the Lie Group SE(3), the Special Euclidean Group (the group of rotations and translations).

This Website

I created this website to experiment with HTML and CSS (in particular Bootstrap), and of course to get in touch with you.

The repo can be accessed below.

Report: An Epidemic as a Sequence of Random Events

Seminar "Stochastics in action" at FU Berlin

With an epidemic as a so-called "motivational" example, the report presents "Walker's Trick" a.k.a. the "Alias method", which allows to pseudo-sample from arbitrary discrete probability distributions.

The report and a Jupyter notebook with an implementation of this method can be accessed below.

Report: The Diffusion Mean

Seminar on Geometric Statistics at FU Berlin

How can we do statistics on manifolds other than Euclidean spaces? This report covers a possible generalisation of means and their estimators to (some) curved manifolds.

The report can be donwloaded below.

Berkeley Project 2: Pacman Maze Deep-Q Learning (Reinforcement/Q-learning)

Artifical Intelligence class at FU Berlin, in collaboration with a fellow student

For details, see the repo below.

Berkeley Project 1: Pacman Maze Search (Search algorithms)

Artifical Intelligence class at FU Berlin, in collaboration with a fellow student

A copy of the original repo can be found below.

Interpetability of Neural Networks

Bachelor thesis

The thesis examines the "Integrated Gradients method" (Sundararajan et al. 2017) from a mathematical standpoint and applies it to a convolutional network classifying X-rays of the chest into the classes "healthy" and "sick". This method consists of comparing the input to a reference input (e.g. the black picture) and to accumulate the gradients along the linear path between these two images.

Further, it is explored on how this could be exploited to create a tool marking conspicous regions in X-rays or other medical images. I measure the accuracy of such a tool by using annotations of physicians as ground truth.

The thesis and the repo with an implementation of this method can be accessed below.