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The recovery of ridge functions on the hypercube suffers from the curse of dimensionality

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arXiv 2019年

作者： Doerr, Benjamin Mayer, Sebastian Ecole Polytechnique CS35003 Palaiseau91120 France Fraunhofer Center for Machine Learning Fraunhofer-Institute for Algo-rithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53754 Germany

A multivariate ridge function is a function of the form f(x) = g(aT x), where g is univariate and a ∈ Rd. We show that the recovery of an unknown ridge function defined on the hypercube [-1, 1]d with Lipschitz-regular profile g suffers from the curse of dimensionality when the recovery error is measured in the L∞-norm, even if we allow randomized algorithms. If a limited number of components of a is substantially larger than the others, then the curse of dimensionality is not present and the problem is weakly tractable provided the profile g is sufficiently regular. Copyright © 2019, The Authors. All rights reserved.

关键词： Recovery

Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids_

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arXiv 2018年

作者： Bohn, Bastian Griebel, Michael Oettershagen, Jens Institute for Numerical Simulation University of Bonn Endenicher Allee 19b Bonn53115 Fraunhofer Center for Machine Learning Fraunhofer Institute for Algorithms and Scien-tific Computing Scai Schloss Birlinghoven Sankt Augustin53754 Germany

For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations of larger (kernel) model classes lead to algo-rithms, which naturally scale linearly in the amount of data points. For moderate-dimensional or high-dimensional regression tasks, these grid-based discretizations suffer from the curse of dimensionality. Here, sparse grid methods have proven to circumvent this problem to a large extent. In this context, space-and dimension-Adaptive sparse grids, which can detect and exploit a given low effective dimensionality of nominally high-dimensional data, are particularly successful. They nevertheless rely on an axis-Aligned structure of the solution and exhibit issues for data with predominantly skewed and rotated coordinates. In this paper we propose a preprocessing approach for these adaptive sparse grid algorithms that determines an optimized, problem-dependent coordinate system and, thus, reduces the effective dimensionality of a given data set in the ANOVA sense. We provide numerical examples on synthetic data as well as real-world data to show how an adaptive sparse grid least squares algorithm benefits from our preprocessing *** Codes 68T05 Copyright © 2018, The Authors. All rights reserved.

关键词： Analysis of variance (ANOVA)

Scalable hyperparameter optimization with lazy Gaussian processes

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arXiv 2020年

作者： Ram, Raju Müller, Sabine Pfreundt, Franz-Josef Gauger, Nicolas R. Keuper, Janis Competence Center High Performance Computing Fraunhofer ITWM Kaiserslautern Germany Fraunhofer Center Machine Learning Germany Scientific Computing Group TU Kaiserslautern Germany Institute for Machine Learning and Analytics Offenburg University Germany

Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious manual (try and error) tuning of these parameters. Due to its very high sample efficiency, Bayesian Optimization over a Gaussian Processes modeling of the parameter space has become the method of choice. Unfortunately, this approach suffers from a cubic compute complexity due to underlying Cholesky factorization, which makes it very hard to be scaled beyond a small number of sampling steps. In this paper, we present a novel, highly accurate approximation of the underlying Gaussian Process. Reducing its computational complexity from cubic to quadratic allows an efficient strong scaling of Bayesian Optimization while outperforming the previous approach regarding optimization accuracy. The first experiments show speedups of a factor of 162 in single node and further speed up by a factor of 5 in a parallel environment. Copyright © 2020, The Authors. All rights reserved.

关键词： Gaussian distribution

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arXiv 2021年

作者： Bulin, Johannes Hamaekers, Jan Department of Virtual Material Design Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany Fraunhofer Center for Machine Learning Schloss Birlinghoven Sankt Augustin53757 Germany

Determining whether two particle systems are similar is a common problem in particle simulations. When the comparison should be invariant under permutations, orthogonal transformations, and translations of the systems, special techniques are needed. We present an algorithm that can test particle systems of finite size for similarity and, if they are similar, can find the optimal alignment between them. Our approach is based on an invariant version of the root mean square deviation (RMSD) measure and is capable of finding the globally optimal solution in O(n3) operations where n is the number of three-dimensional particles. Copyright © 2021, The Authors. All rights reserved.

关键词： machine learning

GradVis: Visualization and Second Order Analysis of Optimization Surfaces during the Training of Deep Neural Networks

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GradVis: Visualization and Second Order Analysis of Optimiza...

IEEE/ACM Workshop on machine learning in High Performance computing Environments (MLHPC)

作者： Avraam Chatzimichailidis Janis Keuper Franz-Josef Pfreundt Nicolas R. Gauger Competence Center High Performance Computing Fraunhofer ITWM Kaiserslautern Germany Chair for Scientific Computing TU Kaiserslautern Kaiserslautern Germany Institute for Machine Learning and Analytics Offenburg University Germany Fraunhofer Center Machine Learning Germany

ISBN: (纸本)9781728159867

Current training methods for deep neural networks boil down to very high dimensional and non-convex optimization problems which are usually solved by a wide range of stochastic gradient descent methods. While these approaches tend to work in practice, there are still many gaps in the theoretical understanding of key aspects like convergence and generalization guarantees, which are induced by the properties of the optimization surface (loss landscape). In order to gain deeper insights, a number of recent publications proposed methods to visualize and analyze the otimization surfaces. However, the computational cost of these methods are very high, making it hardly possible to use them on larger networks. In this paper, we present the GradVis Toolbox, an open source library for efficient and scalable visualization and analysis of deep neural network loss landscapes in Tesorflow and PyTorch. Introducing more efficient mathematical formulations and a novel parallelization scheme, GradVis allows to plot 2d and 3d projections of optimization surfaces and trajectories, as well as high resolution second order gradient information for large networks.

关键词： Visualization Eigenvalues Parallelization Deep-learning Second-order parallelization Visualization eigenvalues Neural network source program library Training Functional training Surfaces Analysis

Compensation of pressure peaks in PWK-type hydraulic pumps

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Key Engineering Materials 2011年 490卷 33-44页

作者： Osiecki, Leszek Patrosz, Piotr Zawistowski, Tomasz Landvogt, Bettina Piechna, Janusz Zyliñski, Bartek Gdansk University of Technology ul. Narutowicza 11/12 80-233 Gdansk Poland Space Research Center Polish Academy of Sciences ul. Bartycka 18A 00-716 Warszawa Poland Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven 53754 Sankt Augustin Germany Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa Poland Bandak Engineering Postboks 1505 Ålesund Norway

Hydraulic axial pumps equipped with cam-driven commutation unit (PWK pumps) proved their high efficiency up to 55 MPa and ability to work self-sucking, even at high speed. Displacement of PWK pump may easily be changed by moving its control cam. Full discharge from hydrostatic forces makes such control possible by direct action of a low-energy actuator like proportional electromagnet or stepping motor. That eliminates heavy and costly hydraulic servomechanism, necessary in other variable displacement machines. Such a control mechanism was positively evaluated in prototype tests in Department of Hydraulics and Pneumatics of Gdañsk University of Technology. The new commutation unit generates however harmful pressure peaks. The paper presents the compensation method for pressure peaks by use of the elastic compensation chamber. It shows also results of multidisciplinary FEA and CFD analysis necessary to properly design the compensation chamber. © 2012 Trans Tech Publications, Switzerland.

关键词： Stepping motors

Scalable Hyperparameter Optimization with Lazy Gaussian Processes

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Scalable Hyperparameter Optimization with Lazy Gaussian Proc...

IEEE/ACM Workshop on machine learning in High Performance computing Environments (MLHPC)

作者： Raju Ram Sabine Müller Franz-Josef Pfreundt Nicolas R. Gauger Janis Keuper Competence Center High Performance Computing Fraunhofer ITWM Kaiserslautern Germany Scientific Computing Group TU Kaiserslautern Germany Fraunhofer ITWM Kaiserslautern Germany Fraunhofer Center Machine Learning Germany Institute for Machine Learning and Analytics Offenburg University Germany

ISBN: (纸本)9781728159867

Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious manual (try and error) tuning of these parameters. Due to its very high sample efficiency, Bayesian Optimization over a Gaussian Processes modeling of the parameter space has become the method of choice. Unfortunately, this approach suffers from a cubic compute complexity due to underlying Cholesky factorization, which makes it very hard to be scaled beyond a small number of sampling steps. In this paper, we present a novel, highly accurate approximation of the underlying Gaussian Process. Reducing its computational complexity from cubic to quadratic allows an efficient strong scaling of Bayesian Optimization while outperforming the previous approach regarding optimization accuracy. First experiments show speedups of a factor of 162 in single node and further speed up by a factor of 5 in a parallel environment.

关键词： Hyper-Parameter optimization Neural architecture search Bayesian optimization Gaussian processes Scalability Gaussian processes Scalability Hyperparameter parameter space methods Cholesky factorisation Cubic Speeding

PHYSICS-INFORMED learning OF AEROSOL MICROPHYSICS

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arXiv 2022年

作者： Harder, Paula Watson-Parris, Duncan Stier, Philip Strassel, Dominik Gauger, Nicolas R. Keuper, Janis Atmospheric Oceanic and Planetary Physics Department of Physics Universty of Oxford United Kingdom Fraunhofer Center High-Performance Computing Fraunhofer ITWM Germany Fraunhofer Center Machine Learning Fraunhofer Society Germany Scientific Computing TU Kaiserslautern Germany Institute for Machine Learning and Analytics

Aerosol particles play an important role in the climate system by absorbing and scattering radiation and influencing cloud properties. They are also one of the biggest sources of uncertainty for climate modeling. Many climate models do not include aerosols in sufficient detail due to computational constraints. In order to represent key processes, aerosol microphysical properties and processes have to be accounted for. This is done in the ECHAM-HAM global climate aerosol model using the M7 microphysics, but high computational costs make it very expensive to run with finer resolution or for a longer time. We aim to use machine learning to emulate the microphysics model at sufficient accuracy and reduce the computational cost by being fast at inference time. The original M7 model is used to generate data of input-output pairs to train a neural network on it. We are able to learn the variables' tendencies achieving an average R2 score of 77.1%. We further explore methods to inform and constrain the neural network with physical knowledge to reduce mass violation and enforce mass positivity. On a GPU we achieve a speed-up of up to over 64x compared to the original model. © 2022, CC BY.

关键词： Aerosols

Improving Distantly Supervised Extraction of Drug-Drug and Protein-Protein Interactions 12

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Improving Distantly Supervised Extraction of Drug-Drug and P...

Conference of The European Chapter of The Association for Computational Linguistics

作者： Tamara Bobic Roman Klinger Philippe Thomas Martin Hofmann-Apitius Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven 53754 Sankt Augustin Germany Bonn-Aachen Center for Information Technology Dahlmannstrasse 2 53113 Bonn Germany Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven 53754 Sankt Augustin Germany Computer Science Institut Humboldt-Universitaet Unter den Linden 6 10099 Berlin Germany

ISBN: (纸本)9781622764907

Relation extraction is frequently and successfully addressed by machine learning methods. The downside of this approach is the need for annotated training data, typically generated in tedious manual, cost intensive work. Distantly supervised approaches make use of weakly annotated data, like automatically annotated corpora. Recent work in the biomedical domain has applied distant supervision for protein-protein interaction (PPI) with reasonable results making use of the IntAct database. Such data is typically noisy and heuristics to filter the data are commonly applied. We propose a constraint to increase the quality of data used for training based on the assumption that no self-interaction of real-world objects are described in sentences. In addition, we make use of the University of Kansas Proteomics Service (KUPS) database. These two steps show an increase of 7 percentage points (pp) for the PPI corpus AIMed. We demonstrate the broad applicability of our approach by using the same workflow for the analysis of drug-drug interactions, utilizing relationships available from the drug database DrugBank. We achieve 37.31 % in F_1 measure without manually annotated training data on an independent test set.

关键词： Protein-Protein Interaction Training data pulse position indicator Drug Interactions Heuristics Manual handling Database