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2019


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Limitations of the empirical Fisher approximation for natural gradient descent

Kunstner, F., Hennig, P., Balles, L.

Advances in Neural Information Processing Systems 32, pages: 4158-4169, (Editors: H. Wallach and H. Larochelle and A. Beygelzimer and F. d’Alché-Buc and E. Fox and R. Garnett), Curran Associates, Inc., 33rd Annual Conference on Neural Information Processing Systems, December 2019 (conference)

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link (url) [BibTex]

2019


link (url) [BibTex]


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Convergence Guarantees for Adaptive Bayesian Quadrature Methods

Kanagawa, M., Hennig, P.

Advances in Neural Information Processing Systems 32, pages: 6234-6245, (Editors: H. Wallach and H. Larochelle and A. Beygelzimer and F. d’Alché-Buc and E. Fox and R. Garnett), Curran Associates, Inc., 33rd Annual Conference on Neural Information Processing Systems, December 2019 (conference)

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link (url) [BibTex]

link (url) [BibTex]


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DeepOBS: A Deep Learning Optimizer Benchmark Suite

Schneider, F., Balles, L., Hennig, P.

7th International Conference on Learning Representations (ICLR), May 2019 (conference)

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link (url) [BibTex]

link (url) [BibTex]


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Fast and Robust Shortest Paths on Manifolds Learned from Data

Arvanitidis, G., Hauberg, S., Hennig, P., Schober, M.

Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), 89, pages: 1506-1515, (Editors: Kamalika Chaudhuri and Masashi Sugiyama), PMLR, April 2019 (conference)

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PDF link (url) [BibTex]

PDF link (url) [BibTex]


Active Probabilistic Inference on Matrices for Pre-Conditioning in Stochastic Optimization
Active Probabilistic Inference on Matrices for Pre-Conditioning in Stochastic Optimization

de Roos, F., Hennig, P.

Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), 89, pages: 1448-1457, (Editors: Kamalika Chaudhuri and Masashi Sugiyama), PMLR, April 2019 (conference)

Abstract
Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way to efficiently construct them. For the stochastic optimization problems that dominate contemporary machine learning, however, this approach is not readily available. We propose an iterative algorithm inspired by classic iterative linear solvers that uses a probabilistic model to actively infer a pre-conditioner in situations where Hessian-projections can only be constructed with strong Gaussian noise. The algorithm is empirically demonstrated to efficiently construct effective pre-conditioners for stochastic gradient descent and its variants. Experiments on problems of comparably low dimensionality show improved convergence. In very high-dimensional problems, such as those encountered in deep learning, the pre-conditioner effectively becomes an automatic learning-rate adaptation scheme, which we also empirically show to work well.

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PDF link (url) [BibTex]

PDF link (url) [BibTex]

2018


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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.

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Paper [BibTex]

2018


Paper [BibTex]


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

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]

2015


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


PDF DOI Project Page [BibTex]


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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]

Web PDF [BibTex]


Probabilistic Line Searches for Stochastic Optimization
Probabilistic Line Searches for Stochastic Optimization

Mahsereci, M., Hennig, P.

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]

Matlab research code link (url) [BibTex]


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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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PDF DOI [BibTex]

PDF DOI [BibTex]

2013


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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)

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PDF [BibTex]

2013


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)

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PDF [BibTex]

PDF [BibTex]


Nonparametric dynamics estimation for time periodic systems
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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PDF DOI [BibTex]

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)

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[BibTex]

[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]

PDF [BibTex]

2012


Quasi-Newton Methods: A New Direction
Quasi-Newton Methods: A New Direction

Hennig, P., Kiefel, M.

In Proceedings of the 29th International Conference on Machine Learning, pages: 25-32, ICML ’12, (Editors: John Langford and Joelle Pineau), Omnipress, New York, NY, USA, ICML, July 2012 (inproceedings)

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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website+code pdf link (url) [BibTex]

2012


website+code pdf link (url) [BibTex]


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Learning Tracking Control with Forward Models

Bócsi, B., Hennig, P., Csató, L., Peters, J.

In pages: 259 -264, IEEE International Conference on Robotics and Automation (ICRA), May 2012 (inproceedings)

Abstract
Performing task-space tracking control on redundant robot manipulators is a difficult problem. When the physical model of the robot is too complex or not available, standard methods fail and machine learning algorithms can have advantages. We propose an adaptive learning algorithm for tracking control of underactuated or non-rigid robots where the physical model of the robot is unavailable. The control method is based on the fact that forward models are relatively straightforward to learn and local inversions can be obtained via local optimization. We use sparse online Gaussian process inference to obtain a flexible probabilistic forward model and second order optimization to find the inverse mapping. Physical experiments indicate that this approach can outperform state-of-the-art tracking control algorithms in this context.

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PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Approximate Gaussian Integration using Expectation Propagation

Cunningham, J., Hennig, P., Lacoste-Julien, S.

In pages: 1-11, -, January 2012 (inproceedings) Submitted

Abstract
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We offer here an empirical study of the utility of Expectation Propagation (EP) as an approximate integration method for this problem. For rectangular integration regions, the approximation is highly accurate. We also extend the derivations to the more general case of polyhedral integration regions. However, we find that in this polyhedral case, EP's answer, though often accurate, can be almost arbitrarily wrong. These unexpected results elucidate an interesting and non-obvious feature of EP not yet studied in detail, both for the problem of Gaussian probabilities and for EP more generally.

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Web [BibTex]

Web [BibTex]


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Kernel Topic Models

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

In Fifteenth International Conference on Artificial Intelligence and Statistics, 22, pages: 511-519, JMLR Proceedings, (Editors: Lawrence, N. D. and Girolami, M.), JMLR.org, AISTATS , 2012 (inproceedings)

Abstract
Latent Dirichlet Allocation models discrete data as a mixture of discrete distributions, using Dirichlet beliefs over the mixture weights. We study a variation of this concept, in which the documents' mixture weight beliefs are replaced with squashed Gaussian distributions. This allows documents to be associated with elements of a Hilbert space, admitting kernel topic models (KTM), modelling temporal, spatial, hierarchical, social and other structure between documents. The main challenge is efficient approximate inference on the latent Gaussian. We present an approximate algorithm cast around a Laplace approximation in a transformed basis. The KTM can also be interpreted as a type of Gaussian process latent variable model, or as a topic model conditional on document features, uncovering links between earlier work in these areas.

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PDF Web [BibTex]

PDF Web [BibTex]