25^{th}NOVEMBER2019

With the rising success of deep neural networks, their reliability in terms of robustness (for example, against various kinds of adversarial examples) and confidence estimates becomes increasingly important. Bayesian neural networks promise to address these issues by directly modeling the uncertainty of the estimated network weights. In this article, I want to give a short introduction of training Bayesian neural networks, covering three recent approaches.

06^{th}NOVEMBER2019

The Heidelberg Laureate Forum brings together young researchers and laureates in computer science and mathematics. During lectures, workshops, panel discussions and social events, the forum fosters personal and scientific exchange with other young researchers as well as laureates. I was incredibly lucky to have the opportunity to participate in the 7th Heidelberg Laureate Forum 2019. In this article, I want to give a short overview of the forum and share some of my impressions.

22^{th}AUGUST2018

A variational auto-encoder trained on corrupted (that is, noisy) examples is called denoising variational auto-encoder. While easily implemented, the underlying mathematical framework changes significantly. As the second article in my series on variational auto-encoders, this article discusses the mathematical background of denoising variational auto-encoders.

15^{th}AUGUST2018

In the third article of my series on variational auto-encoders, I want to discuss categorical variational auto-encoders. This variant allows to learn a latent space of discrete (e.g. categorical or Bernoulli) latent variables. Compared to regular variational auto-encoders, the main challenge lies in deriving a working reparameterization trick for discrete latent variables — the so-called Gumbel trick.

08^{th}AUGUST2018

As part of my master thesis, I made heavy use of variational auto-encoders in order to learn latent spaces of shapes — to later perform shape completion. Overall, I invested a big portion of my time in understanding and implementing different variants of variational auto-encoders. This article, a first in a small series, will deal with the mathematics behind variational auto-encoders. The article covers variational inference in general, the concrete case of variational auto-encoder as well as practical considerations.

12^{th}DECEMBER2017

The Simplex algorithm for solving linear programs implemented in PHP.

12^{th}DECEMBER2017

Common matrix decompositions, including LU, Cholesky and QR decompositions, implemented in PHP; also includes an interactive application to demonstrate and explain the material.

27^{th}SEPTEMBER2017

02^{nd}JUNE2016

In the course of a seminar on “Selected Topics in Image Processing”, I worked on iPiano, an algorithm for non-convex and non-smooth optimization proposed by Ochs et al. [1]. iPiano combines forward-backward splitting with an inertial force. This article presents the corresponding seminar paper including an implementation in C++ with applications to image denoising, image segmentation and compressed sensing.