IAM

Check out our latest research on weakly-supervised 3D shape completion.

TAG»MATHEMATICS«

ARTICLE

Denoising Variational Auto-Encoders

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.

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ARTICLE

Categorical Variational Auto-Encoders and the Gumbel Trick

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.

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ARTICLE

The Mathematics of Variational Auto-Encoders

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.

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12thDECEMBER2017

PROJECT

The Simplex algorithm for solving linear programs implemented in PHP.

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12thDECEMBER2017

PROJECT

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

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ARTICLE

Seminar Paper “iPiano: Inertial Proximal Algorithms for Non-Convex Optimization”

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.

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09thMAY2016

PROJECT

Efficient C++ implementation of iPiano, a proximal algorithm with inertial force for non-convex and non-smooth optimization; including applications to image segmentation.

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