Publications | Max Planck Institute for Intelligent Systems

2016

ei pn Klenske, E. D., Hennig, P., Schölkopf, B., Zeilinger, M. N. Approximate dual control maintaining the value of information with an application to building control In European Control Conference (ECC), pages: 800-806, June 2016 (inproceedings)

Active Uncertainty Calibration in Bayesian ODE Solvers

Kersting, H., Hennig, P.

Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence (UAI), pages: 309-318, (Editors: Ihler, A. and Janzing, D.), AUAI Press, June 2016 (conference)

Abstract

There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al.~introduced a sampling-based class of methods that are `well-calibrated' in a specific sense. But the computational cost of these methods is significantly above that of classic methods. On the other hand, Schober et al.~pointed out a precise connection between classic Runge-Kutta ODE solvers and Gaussian filters, which gives only a rough probabilistic calibration, but at negligible cost overhead. By formulating the solution of ODEs as approximate inference in linear Gaussian SDEs, we investigate a range of probabilistic ODE solvers, that bridge the trade-off between computational cost and probabilistic calibration, and identify the inaccurate gradient measurement as the crucial source of uncertainty. We propose the novel filtering-based method Bayesian Quadrature filtering (BQF) which uses Bayesian quadrature to actively learn the imprecision in the gradient measurement by collecting multiple gradient evaluations.

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ei pn Kersting, H., Hennig, P. Active Uncertainty Calibration in Bayesian ODE Solvers Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence (UAI), pages: 309-318, (Editors: Ihler, A. and Janzing, D.), AUAI Press, June 2016 (conference)

link (url) Project Page [BibTex]

Automatic LQR Tuning Based on Gaussian Process Global Optimization

Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 270-277, IEEE, IEEE International Conference on Robotics and Automation, May 2016 (inproceedings)

Abstract

This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree- of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Results of a two- and four- dimensional tuning problems highlight the method’s potential for automatic controller tuning on robotic platforms.

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Video PDF DOI Project Page [BibTex]

am ics pn Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S. Automatic LQR Tuning Based on Gaussian Process Global Optimization In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 270-277, IEEE, IEEE International Conference on Robotics and Automation, May 2016 (inproceedings)

Video PDF DOI Project Page [BibTex]

Batch Bayesian Optimization via Local Penalization

González, J., Dai, Z., Hennig, P., Lawrence, N.

Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), 51, pages: 648-657, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C.), May 2016 (conference)

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ei pn González, J., Dai, Z., Hennig, P., Lawrence, N. Batch Bayesian Optimization via Local Penalization Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), 51, pages: 648-657, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C.), May 2016 (conference)

link (url) Project Page [BibTex]

Probabilistic Approximate Least-Squares

Bartels, S., Hennig, P.

Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), 51, pages: 676-684, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C. ), May 2016 (conference)

Abstract

Least-squares and kernel-ridge / Gaussian process regression are among the foundational algorithms of statistics and machine learning. Famously, the worst-case cost of exact nonparametric regression grows cubically with the data-set size; but a growing number of approximations have been developed that estimate good solutions at lower cost. These algorithms typically return point estimators, without measures of uncertainty. Leveraging recent results casting elementary linear algebra operations as probabilistic inference, we propose a new approximate method for nonparametric least-squares that affords a probabilistic uncertainty estimate over the error between the approximate and exact least-squares solution (this is not the same as the posterior variance of the associated Gaussian process regressor). This allows estimating the error of the least-squares solution on a subset of the data relative to the full-data solution. The uncertainty can be used to control the computational effort invested in the approximation. Our algorithm has linear cost in the data-set size, and a simple formal form, so that it can be implemented with a few lines of code in programming languages with linear algebra functionality.

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ei pn Bartels, S., Hennig, P. Probabilistic Approximate Least-Squares Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), 51, pages: 676-684, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C. ), May 2016 (conference)

Gaussian Process-Based Predictive Control for Periodic Error Correction

Klenske, E. D., Zeilinger, M., Schölkopf, B., Hennig, P.

IEEE Transactions on Control Systems Technology , 24(1):110-121, 2016 (article)

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ei pn Klenske, E. D., Zeilinger, M., Schölkopf, B., Hennig, P. Gaussian Process-Based Predictive Control for Periodic Error Correction IEEE Transactions on Control Systems Technology , 24(1):110-121, 2016 (article)

Klenske, E. D., Hennig, P.

Dual Control for Approximate Bayesian Reinforcement Learning

Journal of Machine Learning Research, 17(127):1-30, 2016 (article)

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PDF link (url) [BibTex]

ei pn Klenske, E. D., Hennig, P. Dual Control for Approximate Bayesian Reinforcement Learning Journal of Machine Learning Research, 17(127):1-30, 2016 (article)

PDF link (url) [BibTex]

2015

Automatic LQR Tuning Based on Gaussian Process Optimization: Early Experimental Results

Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S.

Machine Learning in Planning and Control of Robot Motion Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems (iROS), pages: , , Machine Learning in Planning and Control of Robot Motion Workshop, October 2015 (conference)

Abstract

This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree-of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Preliminary results of a low-dimensional tuning problem highlight the method’s potential for automatic controller tuning on robotic platforms.

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PDF DOI Project Page [BibTex]

2015

am ei ics pn Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S. Automatic LQR Tuning Based on Gaussian Process Optimization: Early Experimental Results Machine Learning in Planning and Control of Robot Motion Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems (iROS), pages: , , Machine Learning in Planning and Control of Robot Motion Workshop, October 2015 (conference)

PDF DOI Project Page [BibTex]

Inference of Cause and Effect with Unsupervised Inverse Regression

Sgouritsa, E., Janzing, D., Hennig, P., Schölkopf, B.

In Proceedings of the 18th International Conference on Artificial Intelligence and Statistics, 38, pages: 847-855, JMLR Workshop and Conference Proceedings, (Editors: Lebanon, G. and Vishwanathan, S.V.N.), JMLR.org, AISTATS, 2015 (inproceedings)

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Web PDF [BibTex]

ei pn Sgouritsa, E., Janzing, D., Hennig, P., Schölkopf, B. Inference of Cause and Effect with Unsupervised Inverse Regression In Proceedings of the 18th International Conference on Artificial Intelligence and Statistics, 38, pages: 847-855, JMLR Workshop and Conference Proceedings, (Editors: Lebanon, G. and Vishwanathan, S.V.N.), JMLR.org, AISTATS, 2015 (inproceedings)

Web PDF [BibTex]

Probabilistic Interpretation of Linear Solvers

Mahsereci, M., Hennig, P.

SIAM Journal on Optimization, 25(1):234-260, 2015 (article)

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Web PDF link (url) DOI [BibTex]

ei pn Hennig, P. Probabilistic Interpretation of Linear Solvers SIAM Journal on Optimization, 25(1):234-260, 2015 (article)

Web PDF link (url) DOI [BibTex]

Probabilistic Line Searches for Stochastic Optimization

In Advances in Neural Information Processing Systems 28, pages: 181-189, (Editors: C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama and R. Garnett), Curran Associates, Inc., 29th Annual Conference on Neural Information Processing Systems (NIPS), 2015 (inproceedings)

Abstract

In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a probabilistic line search by combining the structure of existing deterministic methods with notions from Bayesian optimization. Our method retains a Gaussian process surrogate of the univariate optimization objective, and uses a probabilistic belief over the Wolfe conditions to monitor the descent. The algorithm has very low computational cost, and no user-controlled parameters. Experiments show that it effectively removes the need to define a learning rate for stochastic gradient descent. [You can find the matlab research code under `attachments' below. The zip-file contains a minimal working example. The docstring in probLineSearch.m contains additional information. A more polished implementation in C++ will be published here at a later point. For comments and questions about the code please write to mmahsereci@tue.mpg.de.]

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Matlab research code link (url) [BibTex]

ei pn Mahsereci, M., Hennig, P. Probabilistic Line Searches for Stochastic Optimization In Advances in Neural Information Processing Systems 28, pages: 181-189, (Editors: C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama and R. Garnett), Curran Associates, Inc., 29th Annual Conference on Neural Information Processing Systems (NIPS), 2015 (inproceedings)

Matlab research code link (url) [BibTex]

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)

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ei pn 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)

Probabilistic numerics and uncertainty in computations

Hennig, P., Osborne, M. A., Girolami, M.

Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2179), 2015 (article)

Abstract

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

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ei pn Hennig, P., Osborne, M. A., Girolami, M. Probabilistic numerics and uncertainty in computations Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2179), 2015 (article)

2013

Camera-specific Image Denoising

Schober, M.

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

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2013

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

website+code pdf link (url) [BibTex]

Quasi-Newton Methods: A New Direction

Hennig, P., Kiefel, M.

Journal of Machine Learning Research, 14(1):843-865, March 2013 (article)

Abstract

Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newton methods can be interpreted as approximations of Bayesian linear regression under varying prior assumptions. This new notion elucidates some shortcomings of classical algorithms, and lights the way to a novel nonparametric quasi-Newton method, which is able to make more efficient use of available information at computational cost similar to its predecessors.

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ei ps pn Hennig, P., Kiefel, M. Quasi-Newton Methods: A New Direction Journal of Machine Learning Research, 14(1):843-865, March 2013 (article)

website+code pdf link (url) [BibTex]

The Randomized Dependence Coefficient

Lopez-Paz, D., Hennig, P., Schölkopf, B.

In Advances in Neural Information Processing Systems 26, pages: 1-9, (Editors: C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K.Q. Weinberger), 27th Annual Conference on Neural Information Processing Systems (NIPS), 2013 (inproceedings)

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ei pn Lopez-Paz, D., Hennig, P., Schölkopf, B. The Randomized Dependence Coefficient In Advances in Neural Information Processing Systems 26, pages: 1-9, (Editors: C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K.Q. Weinberger), 27th Annual Conference on Neural Information Processing Systems (NIPS), 2013 (inproceedings)

Fast Probabilistic Optimization from Noisy Gradients

In Proceedings of The 30th International Conference on Machine Learning, JMLR W&CP 28(1), pages: 62–70, (Editors: S Dasgupta and D McAllester), ICML, 2013 (inproceedings)

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ei pn Hennig, P. Fast Probabilistic Optimization from Noisy Gradients In Proceedings of The 30th International Conference on Machine Learning, JMLR W&CP 28(1), pages: 62–70, (Editors: S Dasgupta and D McAllester), ICML, 2013 (inproceedings)

Nonparametric dynamics estimation for time periodic systems

Klenske, E., Zeilinger, M., Schölkopf, B., Hennig, P.

In Proceedings of the 51st Annual Allerton Conference on Communication, Control, and Computing, pages: 486-493 , 2013 (inproceedings)

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ei pn Klenske, E., Zeilinger, M., Schölkopf, B., Hennig, P. Nonparametric dynamics estimation for time periodic systems In Proceedings of the 51st Annual Allerton Conference on Communication, Control, and Computing, pages: 486-493 , 2013 (inproceedings)

Lopez-Paz, D., Hennig, P., Schölkopf, B.

The Randomized Dependence Coefficient

Neural Information Processing Systems (NIPS), 2013 (poster)

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ei pn Lopez-Paz, D., Hennig, P., Schölkopf, B. The Randomized Dependence Coefficient Neural Information Processing Systems (NIPS), 2013 (poster)

Analytical probabilistic modeling for radiation therapy treatment planning

Bangert, M., Hennig, P., Oelfke, U.

Physics in Medicine and Biology, 58(16):5401-5419, 2013 (article)

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ei pn Bangert, M., Hennig, P., Oelfke, U. Analytical probabilistic modeling for radiation therapy treatment planning Physics in Medicine and Biology, 58(16):5401-5419, 2013 (article)

Analytical probabilistic proton dose calculation and range uncertainties

Bangert, M., Hennig, P., Oelfke, U.

In 17th International Conference on the Use of Computers in Radiation Therapy, pages: 6-11, (Editors: A. Haworth and T. Kron), ICCR, 2013 (inproceedings)

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[BibTex]

ei pn Bangert, M., Hennig, P., Oelfke, U. Analytical probabilistic proton dose calculation and range uncertainties In 17th International Conference on the Use of Computers in Radiation Therapy, pages: 6-11, (Editors: A. Haworth and T. Kron), ICCR, 2013 (inproceedings)

[BibTex]

Animating Samples from Gaussian Distributions

(8), Max Planck Institute for Intelligent Systems, Tübingen, Germany, 2013 (techreport)

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ei pn Hennig, P. Animating Samples from Gaussian Distributions (8), Max Planck Institute for Intelligent Systems, Tübingen, Germany, 2013 (techreport)

2011

Optimal Reinforcement Learning for Gaussian Systems