Sparse Grids in a Nutshell
- J. Garcke
- Computer Science
- 2012
The technique of sparse grids allows to overcome the curse of dimensionality, which prevents the use of classical numerical discretization schemes in more than three or four dimensions, under…
Informed Machine Learning – A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems
- Laura von Rueden, S. Mayer, Jannis Schuecker
- Computer ScienceIEEE Transactions on Knowledge and Data…
- 29 March 2019
A taxonomy is introduced that serves as a classification framework for informed machine learning approaches and considers the source of knowledge, its representation, and its integration into the machine learning pipeline.
Multivariate Regression and Machine Learning with Sums of Separable Functions
- G. Beylkin, J. Garcke, Martin J. Mohlenkamp
- Computer ScienceSIAM Journal on Scientific Computing
- 1 February 2009
An algorithm for learning (or estimating) a function of many variables from scattered data is approximated by a sum of separable functions, following the paradigm of separated representations, which is suitable for large data sets in high dimensions.
Explainable Machine Learning for Scientific Insights and Discoveries
- R. Roscher, B. Bohn, Marco F. Duarte, J. Garcke
- Computer ScienceIEEE Access
- 22 May 2019
This article provides a survey of recent scientific works that incorporate machine learning and the way that explainable machine learning is used in combination with domain knowledge from the application areas and discusses three core elements that were identified as relevant in this context: transparency, interpretability, and explainability.
The combination technique and some generalisations
- M. Hegland, J. Garcke, V. Challis
- Mathematics
- 15 January 2007
On the numerical solution of the chemical master equation with sums of rank one tensors
- M. Hegland, J. Garcke
- Computer Science
- 10 August 2011
It is shown that sums of rank one tensors representing the so-called Candecomp/Parafac or CP-decomposition is used effectively to solve the chemical master equations as in many cases the effective tensor rank of the probability distribution only grows slowly with time.
Data Mining with Sparse Grids
- J. Garcke, M. Griebel, M. Thess
- Computer ScienceComputing
- 1 November 2001
It turns out that the new method achieves correctness rates which are competitive to that of the best existing methods, i.e. the amount of data to be classified.
An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations
- O. Bokanowski, J. Garcke, M. Griebel, Irene Klompmaker
- Computer Science, MathematicsJournal of Scientific Computing
- 1 June 2013
We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models…
Importance Weighted Inductive Transfer Learning for Regression
- J. Garcke, Thomas Vanck
- Computer ScienceECML/PKDD
- 15 September 2014
This work considers inductive transfer learning for dataset shift, a situation in which the distributions of two sampled, but closely related, datasets differ, and proposes two methods for regression based on importance weighting.
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