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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)

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)

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

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)

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.

PDF link (url) [BibTex]

PDF link (url) [BibTex]


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On the positivity and magnitudes of Bayesian quadrature weights

Karvonen, T., Kanagawa, M., Särkä, S.

Statistics and Computing, 29, pages: 1317-1333, 2019 (article)

DOI [BibTex]

DOI [BibTex]


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Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective

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

Statistics and Computing, 29(6):1297-1315, 2019 (article)

DOI [BibTex]


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Dense connectomic reconstruction in layer 4 of the somatosensory cortex

Motta, A., Berning, M., Boergens, K. M., Staffler, B., Beining, M., Loomba, S., Hennig, P., Wissler, H., Helmstaedter, M.

Science, 366(6469):eaay3134, American Association for the Advancement of Science, 2019 (article)

DOI [BibTex]

DOI [BibTex]


Probabilistic Linear Solvers: A Unifying View
Probabilistic Linear Solvers: A Unifying View

Bartels, S., Cockayne, J., Ipsen, I., Hennig, P.

Statistics and Computing, 29(6):1249-1263, 2019 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


Active Uncertainty Calibration in Bayesian ODE Solvers
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.

link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


Automatic LQR Tuning Based on Gaussian Process Global Optimization
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.

Video - Automatic LQR Tuning Based on Gaussian Process Global Optimization - ICRA 2016 Video - Automatic Controller Tuning on a Two-legged Robot PDF DOI Project Page [BibTex]

Video - Automatic LQR Tuning Based on Gaussian Process Global Optimization - ICRA 2016 Video - Automatic Controller Tuning on a Two-legged Robot 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)

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


Probabilistic Approximate Least-Squares
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.

link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


Gaussian Process-Based Predictive Control for Periodic Error Correction
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)

PDF DOI [BibTex]


Dual Control for Approximate Bayesian Reinforcement Learning
Dual Control for Approximate Bayesian Reinforcement Learning

Klenske, E. D., Hennig, P.

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

PDF link (url) [BibTex]

PDF link (url) [BibTex]

2011


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Optimal Reinforcement Learning for Gaussian Systems

Hennig, P.

In Advances in Neural Information Processing Systems 24, pages: 325-333, (Editors: J Shawe-Taylor and RS Zemel and P Bartlett and F Pereira and KQ Weinberger), Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS), 2011 (inproceedings)

Abstract
The exploration-exploitation trade-off is among the central challenges of reinforcement learning. The optimal Bayesian solution is intractable in general. This paper studies to what extent analytic statements about optimal learning are possible if all beliefs are Gaussian processes. A first order approximation of learning of both loss and dynamics, for nonlinear, time-varying systems in continuous time and space, subject to a relatively weak restriction on the dynamics, is described by an infinite-dimensional partial differential equation. An approximate finitedimensional projection gives an impression for how this result may be helpful.

PDF Web [BibTex]

2011

PDF Web [BibTex]

2007


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Point-spread functions for backscattered imaging in the scanning electron microscope

Hennig, P., Denk, W.

Journal of Applied Physics , 102(12):1-8, December 2007 (article)

Abstract
One knows the imaging system's properties are central to the correct interpretation of any image. In a scanning electron microscope regions of different composition generally interact in a highly nonlinear way during signal generation. Using Monte Carlo simulations we found that in resin-embedded, heavy metal-stained biological specimens staining is sufficiently dilute to allow an approximately linear treatment. We then mapped point-spread functions for backscattered-electron contrast, for primary energies of 3 and 7 keV and for different detector specifications. The point-spread functions are surprisingly well confined (both laterally and in depth) compared even to the distribution of only those scattered electrons that leave the sample again.

Web DOI [BibTex]

2007

Web DOI [BibTex]