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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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link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


Thumb xl screen shot 2016 01 19 at 14.48.37
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]

Video PDF DOI Project Page [BibTex]


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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)

ei pn

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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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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link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


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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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PDF DOI [BibTex]

PDF DOI [BibTex]


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Dual Control for Approximate Bayesian Reinforcement Learning

Klenske, E. D., Hennig, P.

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

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PDF link (url) [BibTex]

PDF link (url) [BibTex]


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Extrapolation and learning equations

Martius, G., Lampert, C. H.

2016, arXiv preprint \url{https://arxiv.org/abs/1610.02995} (misc)

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Project Page [BibTex]

Project Page [BibTex]

2014


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Probabilistic Progress Bars

Kiefel, M., Schuler, C., Hennig, P.

In Conference on Pattern Recognition (GCPR), 8753, pages: 331-341, Lecture Notes in Computer Science, (Editors: Jiang, X., Hornegger, J., and Koch, R.), Springer, GCPR, September 2014 (inproceedings)

Abstract
Predicting the time at which the integral over a stochastic process reaches a target level is a value of interest in many applications. Often, such computations have to be made at low cost, in real time. As an intuitive example that captures many features of this problem class, we choose progress bars, a ubiquitous element of computer user interfaces. These predictors are usually based on simple point estimators, with no error modelling. This leads to fluctuating behaviour confusing to the user. It also does not provide a distribution prediction (risk values), which are crucial for many other application areas. We construct and empirically evaluate a fast, constant cost algorithm using a Gauss-Markov process model which provides more information to the user.

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website+code pdf DOI [BibTex]

2014


website+code pdf DOI [BibTex]


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Probabilistic Solutions to Differential Equations and their Application to Riemannian Statistics

Hennig, P., Hauberg, S.

In Proceedings of the 17th International Conference on Artificial Intelligence and Statistics, 33, pages: 347-355, JMLR: Workshop and Conference Proceedings, (Editors: S Kaski and J Corander), Microtome Publishing, Brookline, MA, AISTATS, April 2014 (inproceedings)

Abstract
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian manifolds, where non-analytic ordinary differential equations are involved in virtually all computations. The probabilistic formulation permits marginalising the uncertainty of the numerical solution such that statistics are less sensitive to inaccuracies. This leads to new Riemannian algorithms for mean value computations and principal geodesic analysis. Marginalisation also means results can be less precise than point estimates, enabling a noticeable speed-up over the state of the art. Our approach is an argument for a wider point that uncertainty caused by numerical calculations should be tracked throughout the pipeline of machine learning algorithms.

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pdf Youtube Supplements Project page link (url) [BibTex]

pdf Youtube Supplements Project page link (url) [BibTex]


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Local Gaussian Regression

Meier, F., Hennig, P., Schaal, S.

arXiv preprint, March 2014, clmc (misc)

Abstract
Abstract: Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is that it can work with ...

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Web link (url) [BibTex]

Web link (url) [BibTex]


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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)

ei pn

Web link (url) [BibTex]

Web link (url) [BibTex]


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Active Learning of Linear Embeddings for Gaussian Processes

Garnett, R., Osborne, M., Hennig, P.

In Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, pages: 230-239, (Editors: NL Zhang and J Tian), AUAI Press , Corvallis, Oregon, UAI2014, 2014, another link: http://arxiv.org/abs/1310.6740 (inproceedings)

ei pn

PDF Web [BibTex]

PDF Web [BibTex]


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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)

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DOI [BibTex]

DOI [BibTex]


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Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature

Gunter, T., Osborne, M., Garnett, R., Hennig, P., Roberts, S.

In Advances in Neural Information Processing Systems 27, pages: 2789-2797, (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)

ei pn

Web link (url) [BibTex]

Web link (url) [BibTex]


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Incremental Local Gaussian Regression

Meier, F., Hennig, P., Schaal, S.

In Advances in Neural Information Processing Systems 27, pages: 972-980, (Editors: Z. Ghahramani, M. Welling, C. Cortes, N.D. Lawrence and K.Q. Weinberger), 28th Annual Conference on Neural Information Processing Systems (NIPS), 2014, clmc (inproceedings)

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PDF link (url) [BibTex]

PDF link (url) [BibTex]


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Efficient Bayesian Local Model Learning for Control

Meier, F., Hennig, P., Schaal, S.

In Proceedings of the IEEE International Conference on Intelligent Robots and Systems, pages: 2244 - 2249, IROS, 2014, clmc (inproceedings)

Abstract
Model-based control is essential for compliant controland force control in many modern complex robots, like humanoidor disaster robots. Due to many unknown and hard tomodel nonlinearities, analytical models of such robots are oftenonly very rough approximations. However, modern optimizationcontrollers frequently depend on reasonably accurate models,and degrade greatly in robustness and performance if modelerrors are too large. For a long time, machine learning hasbeen expected to provide automatic empirical model synthesis,yet so far, research has only generated feasibility studies butno learning algorithms that run reliably on complex robots.In this paper, we combine two promising worlds of regressiontechniques to generate a more powerful regression learningsystem. On the one hand, locally weighted regression techniquesare computationally efficient, but hard to tune due to avariety of data dependent meta-parameters. On the other hand,Bayesian regression has rather automatic and robust methods toset learning parameters, but becomes quickly computationallyinfeasible for big and high-dimensional data sets. By reducingthe complexity of Bayesian regression in the spirit of local modellearning through variational approximations, we arrive at anovel algorithm that is computationally efficient and easy toinitialize for robust learning. Evaluations on several datasetsdemonstrate very good learning performance and the potentialfor a general regression learning tool for robotics.

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PDF link (url) DOI [BibTex]

PDF link (url) DOI [BibTex]


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Self-Exploration of the Stumpy Robot with Predictive Information Maximization

Martius, G., Jahn, L., Hauser, H., V. Hafner, V.

In Proc. From Animals to Animats, SAB 2014, 8575, pages: 32-42, LNCS, Springer, 2014 (inproceedings)

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[BibTex]

[BibTex]


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Robot Learning by Guided Self-Organization

Martius, G., Der, R., Herrmann, J. M.

In Guided Self-Organization: Inception, 9, pages: 223-260, Emergence, Complexity and Computation, Springer Berlin Heidelberg, 2014 (incollection)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2010


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Using an Infinite Von Mises-Fisher Mixture Model to Cluster Treatment Beam Directions in External Radiation Therapy

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

In pages: 746-751 , (Editors: Draghici, S. , T.M. Khoshgoftaar, V. Palade, W. Pedrycz, M.A. Wani, X. Zhu), IEEE, Piscataway, NJ, USA, Ninth International Conference on Machine Learning and Applications (ICMLA), December 2010 (inproceedings)

Abstract
We present a method for fully automated selection of treatment beam ensembles for external radiation therapy. We reformulate the beam angle selection problem as a clustering problem of locally ideal beam orientations distributed on the unit sphere. For this purpose we construct an infinite mixture of von Mises-Fisher distributions, which is suited in general for density estimation from data on the D-dimensional sphere. Using a nonparametric Dirichlet process prior, our model infers probability distributions over both the number of clusters and their parameter values. We describe an efficient Markov chain Monte Carlo inference algorithm for posterior inference from experimental data in this model. The performance of the suggested beam angle selection framework is illustrated for one intra-cranial, pancreas, and prostate case each. The infinite von Mises-Fisher mixture model (iMFMM) creates between 18 and 32 clusters, depending on the patient anatomy. This suggests to use the iMFMM directly for beam ensemble selection in robotic radio surgery, or to generate low-dimensional input for both subsequent optimization of trajectories for arc therapy and beam ensemble selection for conventional radiation therapy.

ei pn

Web DOI [BibTex]

2010


Web DOI [BibTex]


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Coherent Inference on Optimal Play in Game Trees

Hennig, P., Stern, D., Graepel, T.

In JMLR Workshop and Conference Proceedings Volume 9: AISTATS 2010, pages: 326-333, (Editors: Teh, Y.W. , M. Titterington ), JMLR, Cambridge, MA, USA, Thirteenth International Conference on Artificial Intelligence and Statistics, May 2010 (inproceedings)

Abstract
Round-based games are an instance of discrete planning problems. Some of the best contemporary game tree search algorithms use random roll-outs as data. Relying on a good policy, they learn on-policy values by propagating information upwards in the tree, but not between sibling nodes. Here, we present a generative model and a corresponding approximate message passing scheme for inference on the optimal, off-policy value of nodes in smooth AND/OR trees, given random roll-outs. The crucial insight is that the distribution of values in game trees is not completely arbitrary. We define a generative model of the on-policy values using a latent score for each state, representing the value under the random roll-out policy. Inference on the values under the optimal policy separates into an inductive, pre-data step and a deductive, post-data part. Both can be solved approximately with Expectation Propagation, allowing off-policy value inference for any node in the (exponentially big) tree in linear time.

ei pn

PDF Web [BibTex]

PDF Web [BibTex]


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Goal-Oriented Control of Self-Organizing Behavior in Autonomous Robots

Martius, G.

Georg-August-Universität Göttingen, 2010 (phdthesis)

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link (url) [BibTex]


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\textscLpzRobots: A free and powerful robot simulator

Martius, G., Hesse, F., Güttler, F., Der, R.

\urlhttp://robot.informatik.uni-leipzig.de/software, 2010 (misc)

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[BibTex]

[BibTex]


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Playful Machines: Tutorial

Der, R., Martius, G.

\urlhttp://robot.informatik.uni-leipzig.de/tutorial?lang=en, 2010 (misc)

al

[BibTex]

[BibTex]


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Taming the Beast: Guided Self-organization of Behavior in Autonomous Robots

Martius, G., Herrmann, J. M.

In From Animals to Animats 11, 6226, pages: 50-61, LNCS, Springer, 2010 (incollection)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]