Michael Schober

Ph.D. Student

Probabilistic Numerics

Office: S2.018
Max-Planck-Ring 4
72076 Tübingen
Germany

+49 7071 601 588

+49 7071 601 552

Advisor(s):
Philipp Hennig

Overview
Publications

Together with my supervisor Philipp Hennig and my colleagues, I am working on probabilistic numerics and, more specifically, on using Gaussian Process models for solving Differential Equations. Prior to that, I have been writing my diploma thesis on Image Denoising applied to astronomical images. This work was done under the supervision of Bernhard Schölkopf.

7 results (View BibTeX file of all listed publications)

2018

A probabilistic model for the numerical solution of initial value problems

Schober, M., Särkkä, S., Philipp Hennig,

Statistics and Computing, Springer US, 2018 (article)

Abstract

We study connections between ordinary differential equation (ODE) solvers and probabilistic regression methods in statistics. We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics. Adding to this picture, we show that several multistep methods of Nordsieck form can be recast as Kalman filtering on q-times integrated Wiener processes. Doing so provides a family of IVP solvers that return a Gaussian posterior measure, rather than a point estimate. We show that some such methods have low computational overhead, nontrivial convergence order, and that the posterior has a calibrated concentration rate. Additionally, we suggest a step size adaptation algorithm which completes the proposed method to a practically useful implementation, which we experimentally evaluate using a representative set of standard codes in the DETEST benchmark set.

PDF Code DOI Project Page [BibTex]

2018

Schober, M., Särkkä, S., Philipp Hennig, A probabilistic model for the numerical solution of initial value problems Statistics and Computing, Springer US, 2018 (article)

PDF Code DOI Project Page [BibTex]

Probabilistic Ordinary Differential Equation Solvers — Theory and Applications

Schober, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

[BibTex]

Schober, M. Probabilistic Ordinary Differential Equation Solvers — Theory and Applications Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

[BibTex]

2017

Dynamic Time-of-Flight

Schober, M., Adam, A., Yair, O., Mazor, S., Nowozin, S.

Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2017, pages: 170-179, IEEE, Piscataway, NJ, USA, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017 (conference)

DOI [BibTex]

2017

Schober, M., Adam, A., Yair, O., Mazor, S., Nowozin, S. Dynamic Time-of-Flight Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2017, pages: 170-179, IEEE, Piscataway, NJ, USA, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017 (conference)

DOI [BibTex]

2015

A Random Riemannian Metric for Probabilistic Shortest-Path Tractography

Hauberg, S., Schober, M., Liptrot, M., Hennig, P., Feragen, A.

In 18th International Conference on Medical Image Computing and Computer Assisted Intervention, 9349, pages: 597-604, Lecture Notes in Computer Science, MICCAI, 2015 (inproceedings)

PDF DOI [BibTex]

2015

Hauberg, S., Schober, M., Liptrot, M., Hennig, P., Feragen, A. A Random Riemannian Metric for Probabilistic Shortest-Path Tractography In 18th International Conference on Medical Image Computing and Computer Assisted Intervention, 9349, pages: 597-604, Lecture Notes in Computer Science, MICCAI, 2015 (inproceedings)

PDF DOI [BibTex]

2014

Probabilistic ODE Solvers with Runge-Kutta Means

Schober, M., Duvenaud, D., Hennig, P.

In Advances in Neural Information Processing Systems 27, pages: 739-747, (Editors: Z. Ghahramani, M. Welling, C. Cortes, N.D. Lawrence and K.Q. Weinberger), Curran Associates, Inc., 28th Annual Conference on Neural Information Processing Systems (NIPS), 2014 (inproceedings)

Web link (url) [BibTex]

2014

Schober, M., Duvenaud, D., Hennig, P. Probabilistic ODE Solvers with Runge-Kutta Means In Advances in Neural Information Processing Systems 27, pages: 739-747, (Editors: Z. Ghahramani, M. Welling, C. Cortes, N.D. Lawrence and K.Q. Weinberger), Curran Associates, Inc., 28th Annual Conference on Neural Information Processing Systems (NIPS), 2014 (inproceedings)

Web link (url) [BibTex]

Probabilistic Shortest Path Tractography in DTI Using Gaussian Process ODE Solvers

Schober, M., Kasenburg, N., Feragen, A., Hennig, P., Hauberg, S.

In Medical Image Computing and Computer-Assisted Intervention – MICCAI 2014, Lecture Notes in Computer Science Vol. 8675, pages: 265-272, (Editors: P. Golland, N. Hata, C. Barillot, J. Hornegger and R. Howe), Springer, Heidelberg, MICCAI, 2014 (inproceedings)

DOI [BibTex]

Schober, M., Kasenburg, N., Feragen, A., Hennig, P., Hauberg, S. Probabilistic Shortest Path Tractography in DTI Using Gaussian Process ODE Solvers In Medical Image Computing and Computer-Assisted Intervention – MICCAI 2014, Lecture Notes in Computer Science Vol. 8675, pages: 265-272, (Editors: P. Golland, N. Hata, C. Barillot, J. Hornegger and R. Howe), Springer, Heidelberg, MICCAI, 2014 (inproceedings)

DOI [BibTex]

2013

Camera-specific Image Denoising

Schober, M.

Eberhard Karls Universität Tübingen, Germany, October 2013 (diplomathesis)

PDF [BibTex]

2013

Schober, M. Camera-specific Image Denoising Eberhard Karls Universität Tübingen, Germany, October 2013 (diplomathesis)

PDF [BibTex]

Michael Schober

2018

A probabilistic model for the numerical solution of initial value problems

2018

Probabilistic Ordinary Differential Equation Solvers — Theory and Applications

2017

Dynamic Time-of-Flight

2017

2015

A Random Riemannian Metric for Probabilistic Shortest-Path Tractography

2015

2014

Probabilistic ODE Solvers with Runge-Kutta Means

2014

Probabilistic Shortest Path Tractography in DTI Using Gaussian Process ODE Solvers

2013

Camera-specific Image Denoising

2013

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