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26 results (View BibTeX file of all listed publications)

2018

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Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

Tronarp, F., Kersting, H., Särkkä, S., Hennig, P.

ArXiv preprint 2018, arXiv:1810.03440 [stat.ME], October 2018 (article)

Abstract
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consists of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP---which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a Bayesian state estimation problem and all widely-used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers, which were formulated in terms of generating synthetic measurements of the vector field, come out as specific approximations. We derive novel solvers, both Gaussian and non-Gaussian, from the Bayesian state estimation problem posed in this paper and compare them with other probabilistic solvers in illustrative experiments.

pn

link (url) Project Page [BibTex]

2018

pn Tronarp, F., Kersting, H., Särkkä, S., Hennig, P. Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective ArXiv preprint 2018, arXiv:1810.03440 [stat.ME], October 2018 (article)

link (url) Project Page [BibTex]

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Kernel Recursive ABC: Point Estimation with Intractable Likelihood

Kajihara, T., Kanagawa, M., Yamazaki, K., Fukumizu, K.

Proceedings of the 35th International Conference on Machine Learning, pages: 2405-2414, PMLR, July 2018 (conference)

Abstract
We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why the approach works, showing (for the population setting) that, under a certain assumption, point estimates obtained with this method converge to the true parameter, as recursion proceeds. We have conducted a variety of numerical experiments, including parameter estimation for a real-world pedestrian flow simulator, and show that in most cases our method outperforms existing approaches.

pn

Paper [BibTex]

pn Kajihara, T., Kanagawa, M., Yamazaki, K., Fukumizu, K. Kernel Recursive ABC: Point Estimation with Intractable Likelihood Proceedings of the 35th International Conference on Machine Learning, pages: 2405-2414, PMLR, July 2018 (conference)

Paper [BibTex]

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Convergence Rates of Gaussian ODE Filters

Kersting, H., Sullivan, T. J., Hennig, P.

arXiv preprint 2018, arXiv:1807.09737 [math.NA], July 2018 (article)

Abstract
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives a priori as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. We prove worst-case local convergence rates of order $h^{q+1}$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $h^q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyse how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we present explicit formulas for the steady states and show that the posterior confidence intervals are well calibrated in all considered cases that exhibit global convergence---in the sense that they globally contract at the same rate as the truncation error.

pn

link (url) Project Page [BibTex]

pn Kersting, H., Sullivan, T. J., Hennig, P. Convergence Rates of Gaussian ODE Filters arXiv preprint 2018, arXiv:1807.09737 [math.NA], July 2018 (article)

link (url) Project Page [BibTex]

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Oncilla robot: a versatile open-source quadruped research robot with compliant pantograph legs

Sproewitz, A., Tuleu, A., Ajallooeian, M., Vespignani, M., Moeckel, R., Eckert, P., D’Haene, M., Degrave, J., Nordmann, A., Schrauwen, B., Steil, J., Ijspeert, A. J.

Frontiers in Robotics and AI, 5(67), June 2018, arXiv: 1803.06259 (article)

Abstract
We present Oncilla robot, a novel mobile, quadruped legged locomotion machine. This large-cat sized, 5.1 robot is one of a kind of a recent, bioinspired legged robot class designed with the capability of model-free locomotion control. Animal legged locomotion in rough terrain is clearly shaped by sensor feedback systems. Results with Oncilla robot show that agile and versatile locomotion is possible without sensory signals to some extend, and tracking becomes robust when feedback control is added (Ajaoolleian 2015). By incorporating mechanical and control blueprints inspired from animals, and by observing the resulting robot locomotion characteristics, we aim to understand the contribution of individual components. Legged robots have a wide mechanical and control design parameter space, and a unique potential as research tools to investigate principles of biomechanics and legged locomotion control. But the hardware and controller design can be a steep initial hurdle for academic research. To facilitate the easy start and development of legged robots, Oncilla-robot's blueprints are available through open-source. [...]

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link (url) DOI Project Page [BibTex]

dlg Sproewitz, A., Tuleu, A., Ajallooeian, M., Vespignani, M., Moeckel, R., Eckert, P., D’Haene, M., Degrave, J., Nordmann, A., Schrauwen, B., Steil, J., Ijspeert, A. J. Oncilla robot: a versatile open-source quadruped research robot with compliant pantograph legs Frontiers in Robotics and AI, 5(67), June 2018, arXiv: 1803.06259 (article)

link (url) DOI Project Page [BibTex]

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Learning from Outside the Viability Kernel: Why we Should Build Robots that can Fail with Grace

Heim, S., Sproewitz, A.

Proceedings of SIMPAR 2018, pages: 55-61, IEEE, 2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR), May 2018 (conference)

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link (url) DOI Project Page [BibTex]

dlg Heim, S., Sproewitz, A. Learning from Outside the Viability Kernel: Why we Should Build Robots that can Fail with Grace Proceedings of SIMPAR 2018, pages: 55-61, IEEE, 2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR), May 2018 (conference)

link (url) DOI Project Page [BibTex]

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Impact of Trunk Orientation for Dynamic Bipedal Locomotion

Drama, O.

Dynamic Walking Conference, May 2018 (talk)

Abstract
Impact of trunk orientation for dynamic bipedal locomotion My research revolves around investigating the functional demands of bipedal running, with focus on stabilizing trunk orientation. When we think about postural stability, there are two critical questions we need to answer: What are the necessary and sufficient conditions to achieve and maintain trunk stability? I am concentrating on how morphology affects control strategies in achieving trunk stability. In particular, I denote the trunk pitch as the predominant morphology parameter and explore the requirements it imposes on a chosen control strategy. To analyze this, I use a spring loaded inverted pendulum model extended with a rigid trunk, which is actuated by a hip motor. The challenge for the controller design here is to have a single hip actuator to achieve two coupled tasks of moving the legs to generate motion and stabilizing the trunk. I enforce orthograde and pronograde postures and aim to identify the effect of these trunk orientations on the hip torque and ground reaction profiles for different control strategies.

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Impact of trunk orientation for dynamic bipedal locomotion [DW 2018] link (url) Project Page [BibTex]

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Shaping in Practice: Training Wheels to Learn Fast Hopping Directly in Hardware

Heim, S., Ruppert, F., Sarvestani, A., Sproewitz, A.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2018, pages: 5076-5081, IEEE, International Conference on Robotics and Automation, May 2018 (inproceedings)

Abstract
Learning instead of designing robot controllers can greatly reduce engineering effort required, while also emphasizing robustness. Despite considerable progress in simulation, applying learning directly in hardware is still challenging, in part due to the necessity to explore potentially unstable parameters. We explore the of concept shaping the reward landscape with training wheels; temporary modifications of the physical hardware that facilitate learning. We demonstrate the concept with a robot leg mounted on a boom learning to hop fast. This proof of concept embodies typical challenges such as instability and contact, while being simple enough to empirically map out and visualize the reward landscape. Based on our results we propose three criteria for designing effective training wheels for learning in robotics.

dlg

Video Youtube link (url) Project Page [BibTex]

dlg Heim, S., Ruppert, F., Sarvestani, A., Sproewitz, A. Shaping in Practice: Training Wheels to Learn Fast Hopping Directly in Hardware In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2018, pages: 5076-5081, IEEE, International Conference on Robotics and Automation, May 2018 (inproceedings)

Video Youtube link (url) Project Page [BibTex]

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Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

Kanagawa, M., Hennig, P., Sejdinovic, D., Sriperumbudur, B. K.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

pn

arXiv [BibTex]

pn Kanagawa, M., Hennig, P., Sejdinovic, D., Sriperumbudur, B. K. Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

arXiv [BibTex]

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Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients

Balles, L., Hennig, P.

In Proceedings of the 35th International Conference on Machine Learning (ICML), 2018 (inproceedings) Accepted

Abstract
The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn't. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the sign of stochastic gradients, whereas the update magnitude is determined by an estimate of their relative variance. We disentangle these two aspects and analyze them in isolation, gaining insight into the mechanisms underlying ADAM. This analysis also extends recent results on adverse effects of ADAM on generalization, isolating the sign aspect as the problematic one. Transferring the variance adaptation to SGD gives rise to a novel method, completing the practitioner's toolbox for problems where ADAM fails.

pn

link (url) Project Page [BibTex]

pn Balles, L., Hennig, P. Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients In Proceedings of the 35th International Conference on Machine Learning (ICML), 2018 (inproceedings) Accepted

link (url) Project Page [BibTex]

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Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper introduces a novel Hilbert space representation of a counterfactual distribution---called counterfactual mean embedding (CME)---with applications in nonparametric causal inference. Counterfactual prediction has become an ubiquitous tool in machine learning applications, such as online advertisement, recommendation systems, and medical diagnosis, whose performance relies on certain interventions. To infer the outcomes of such interventions, we propose to embed the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel. Under appropriate assumptions, the CME allows us to perform causal inference over the entire landscape of the counterfactual distribution. The CME can be estimated consistently from observational data without requiring any parametric assumption about the underlying distributions. We also derive a rate of convergence which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Our framework can deal with not only real-valued outcome, but potentially also more complex and structured outcomes such as images, sequences, and graphs. Lastly, our experimental results on off-policy evaluation tasks demonstrate the advantages of the proposed estimator.

ei pn

arXiv [BibTex]

ei pn Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S. Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

arXiv [BibTex]

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Model-based Kernel Sum Rule: Kernel Bayesian Inference with Probabilistic Models

Nishiyama, Y., Kanagawa, M., Gretton, A., Fukumizu, K.

Arxiv e-prints, arXiv:1409.5178v2 [stat.ML], 2018 (article)

Abstract
Kernel Bayesian inference is a powerful nonparametric approach to performing Bayesian inference in reproducing kernel Hilbert spaces or feature spaces. In this approach, kernel means are estimated instead of probability distributions, and these estimates can be used for subsequent probabilistic operations (as for inference in graphical models) or in computing the expectations of smooth functions, for instance. Various algorithms for kernel Bayesian inference have been obtained by combining basic rules such as the kernel sum rule (KSR), kernel chain rule, kernel product rule and kernel Bayes' rule. However, the current framework only deals with fully nonparametric inference (i.e., all conditional relations are learned nonparametrically), and it does not allow for flexible combinations of nonparametric and parametric inference, which are practically important. Our contribution is in providing a novel technique to realize such combinations. We introduce a new KSR referred to as the model-based KSR (Mb-KSR), which employs the sum rule in feature spaces under a parametric setting. Incorporating the Mb-KSR into existing kernel Bayesian framework provides a richer framework for hybrid (nonparametric and parametric) kernel Bayesian inference. As a practical application, we propose a novel filtering algorithm for state space models based on the Mb-KSR, which combines the nonparametric learning of an observation process using kernel mean embedding and the additive Gaussian noise model for a state transition process. While we focus on additive Gaussian noise models in this study, the idea can be extended to other noise models, such as the Cauchy and alpha-stable noise models.

pn

arXiv [BibTex]

pn Nishiyama, Y., Kanagawa, M., Gretton, A., Fukumizu, K. Model-based Kernel Sum Rule: Kernel Bayesian Inference with Probabilistic Models Arxiv e-prints, arXiv:1409.5178v2 [stat.ML], 2018 (article)

arXiv [BibTex]

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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.

pn

PDF Code DOI Project Page [BibTex]

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Probabilistic Approaches to Stochastic Optimization

Mahsereci, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

ei pn

link (url) Project Page [BibTex]

ei pn Mahsereci, M. Probabilistic Approaches to Stochastic Optimization Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

link (url) Project Page [BibTex]

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Probabilistic Ordinary Differential Equation Solvers — Theory and Applications

Schober, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

ei pn

[BibTex]

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

[BibTex]

2013

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Camera-specific Image Denoising

Schober, M.

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

ei pn

PDF [BibTex]

2013

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

PDF [BibTex]

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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.

ei ps pn

website+code pdf link (url) [BibTex]

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]

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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)

ei pn

PDF [BibTex]

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)

PDF [BibTex]

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Fast Probabilistic Optimization from Noisy Gradients

Hennig, P.

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)

ei pn

PDF [BibTex]

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)

PDF [BibTex]

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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)

ei pn

PDF DOI [BibTex]

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)

PDF DOI [BibTex]

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The Randomized Dependence Coefficient

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

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

ei pn

PDF [BibTex]

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

PDF [BibTex]

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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)

ei pn

PDF DOI [BibTex]

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)

PDF DOI [BibTex]

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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)

ei pn

[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]

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Animating Samples from Gaussian Distributions

Hennig, P.

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

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PDF [BibTex]

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

PDF [BibTex]