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2018


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Deep Reinforcement Learning for Event-Triggered Control

Baumann, D., Zhu, J., Martius, G., Trimpe, S.

In Proceedings of the 57th IEEE International Conference on Decision and Control (CDC), pages: 943-950, 57th IEEE International Conference on Decision and Control (CDC), December 2018 (inproceedings)

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arXiv PDF DOI Project Page Project Page [BibTex]

2018


arXiv PDF DOI Project Page Project Page [BibTex]


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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]


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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]

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]

link (url) Project Page [BibTex]


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Nonlinear decoding of a complex movie from the mammalian retina

Botella-Soler, V., Deny, S., Martius, G., Marre, O., Tkačik, G.

PLOS Computational Biology, 14(5):1-27, Public Library of Science, May 2018 (article)

Abstract
Author summary Neurons in the retina transform patterns of incoming light into sequences of neural spikes. We recorded from ∼100 neurons in the rat retina while it was stimulated with a complex movie. Using machine learning regression methods, we fit decoders to reconstruct the movie shown from the retinal output. We demonstrated that retinal code can only be read out with a low error if decoders make use of correlations between successive spikes emitted by individual neurons. These correlations can be used to ignore spontaneous spiking that would, otherwise, cause even the best linear decoders to “hallucinate” nonexistent stimuli. This work represents the first high resolution single-trial full movie reconstruction and suggests a new paradigm for separating spontaneous from stimulus-driven neural activity.

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DOI [BibTex]

DOI [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]

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]

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]

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]

arXiv [BibTex]


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L4: Practical loss-based stepsize adaptation for deep learning

Rolinek, M., Martius, G.

In Advances in Neural Information Processing Systems 31 (NeurIPS 2018), pages: 6434-6444, (Editors: S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett), Curran Associates, Inc., 2018 (inproceedings)

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Github link (url) Project Page [BibTex]

Github link (url) Project Page [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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Systematic self-exploration of behaviors for robots in a dynamical systems framework

Pinneri, C., Martius, G.

In Proc. Artificial Life XI, pages: 319-326, MIT Press, Cambridge, MA, 2018 (inproceedings)

Abstract
One of the challenges of this century is to understand the neural mechanisms behind cognitive control and learning. Recent investigations propose biologically plausible synaptic mechanisms for self-organizing controllers, in the spirit of Hebbian learning. In particular, differential extrinsic plasticity (DEP) [Der and Martius, PNAS 2015], has proven to enable embodied agents to self-organize their individual sensorimotor development, and generate highly coordinated behaviors during their interaction with the environment. These behaviors are attractors of a dynamical system. In this paper, we use the DEP rule to generate attractors and we combine it with a “repelling potential” which allows the system to actively explore all its attractor behaviors in a systematic way. With a view to a self-determined exploration of goal-free behaviors, our framework enables switching between different motion patterns in an autonomous and sequential fashion. Our algorithm is able to recover all the attractor behaviors in a toy system and it is also effective in two simulated environments. A spherical robot discovers all its major rolling modes and a hexapod robot learns to locomote in 50 different ways in 30min.

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link (url) DOI Project Page [BibTex]

link (url) 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]

link (url) Project Page [BibTex]


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Learning equations for extrapolation and control

Sahoo, S. S., Lampert, C. H., Martius, G.

In Proc. 35th International Conference on Machine Learning, ICML 2018, Stockholm, Sweden, 2018, 80, pages: 4442-4450, http://proceedings.mlr.press/v80/sahoo18a/sahoo18a.pdf, (Editors: Dy, Jennifer and Krause, Andreas), PMLR, 2018 (inproceedings)

Abstract
We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.

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Code Arxiv Poster Slides link (url) Project Page [BibTex]

Code Arxiv Poster Slides link (url) Project Page [BibTex]


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Robust Affordable 3D Haptic Sensation via Learning Deformation Patterns

Sun, H., Martius, G.

Proceedings International Conference on Humanoid Robots, pages: 846-853, IEEE, New York, NY, USA, 2018 IEEE-RAS International Conference on Humanoid Robots, 2018, Oral Presentation (conference)

Abstract
Haptic sensation is an important modality for interacting with the real world. This paper proposes a general framework of inferring haptic forces on the surface of a 3D structure from internal deformations using a small number of physical sensors instead of employing dense sensor arrays. Using machine learning techniques, we optimize the sensor number and their placement and are able to obtain high-precision force inference for a robotic limb using as few as 9 sensors. For the optimal and sparse placement of the measurement units (strain gauges), we employ data-driven methods based on data obtained by finite element simulation. We compare data-driven approaches with model-based methods relying on geometric distance and information criteria such as Entropy and Mutual Information. We validate our approach on a modified limb of the “Poppy” robot [1] and obtain 8 mm localization precision.

al

DOI Project Page [BibTex]

DOI 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]

[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.

ei ps pn

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.

ei ps pn

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)

ei pn

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)

am ei pn

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)

al

[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]

2006


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Let It Roll – Emerging Sensorimotor Coordination in a Spherical Robot

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

In Proc, Artificial Life X, pages: 192-198, Intl. Society for Artificial Life, MIT Press, August 2006 (inproceedings)

al

[BibTex]

2006


[BibTex]


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From Motor Babbling to Purposive Actions: Emerging Self-exploration in a Dynamical Systems Approach to Early Robot Development

Der, R., Martius, G.

In Proc. From Animals to Animats 9, SAB 2006, 4095, pages: 406-421, LNCS, Springer, 2006 (inproceedings)

Abstract
Self-organization and the phenomenon of emergence play an essential role in living systems and form a challenge to artificial life systems. This is not only because systems become more lifelike, but also since self-organization may help in reducing the design efforts in creating complex behavior systems. The present paper studies self-exploration based on a general approach to the self-organization of behavior, which has been developed and tested in various examples in recent years. This is a step towards autonomous early robot development. We consider agents under the close sensorimotor coupling paradigm with a certain cognitive ability realized by an internal forward model. Starting from tabula rasa initial conditions we overcome the bootstrapping problem and show emerging self-exploration. Apart from that, we analyze the effect of limited actions, which lead to deprivation of the world model. We show that our paradigm explicitly avoids this by producing purposive actions in a natural way. Examples are given using a simulated simple wheeled robot and a spherical robot driven by shifting internal masses.

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[BibTex]

[BibTex]


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Rocking Stamper and Jumping Snake from a Dynamical System Approach to Artificial Life

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

Adaptive Behavior, 14(2):105-115, 2006 (article)

Abstract
Dynamical systems offer intriguing possibilities as a substrate for the generation of behavior because of their rich behavioral complexity. However this complexity together with the largely covert relation between the parameters and the behavior of the agent is also the main hindrance in the goal-oriented design of a behavior system. This paper presents a general approach to the self-regulation of dynamical systems so that the design problem is circumvented. We consider the controller (a neural net work) as the mediator for changes in the sensor values over time and define a dynamics for the parameters of the controller by maximizing the dynamical complexity of the sensorimotor loop under the condition that the consequences of the actions taken are still predictable. This very general principle is given a concrete mathematical formulation and is implemented in an extremely robust and versatile algorithm for the parameter dynamics of the controller. We consider two different applications, a mechanical device called the rocking stamper and the ODE simulations of a "snake" with five degrees of freedom. In these and many other examples studied we observed various behavior modes of high dynamical complexity.

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DOI [BibTex]

DOI [BibTex]