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Sparse Grids in a Nutshell
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, underExpand
Multivariate Regression and Machine Learning with Sums of Separable Functions
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. Expand
Data Mining with Sparse Grids
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. Expand
An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations
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 modelsExpand
The combination technique and some generalisations
The combination technique has repeatedly been shown to be an effective tool for the approximation with sparse grid spaces. Little is known about the reasons of this effectiveness and in some casesExpand
Sparse Grids and Applications
This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011 and presents recent advances in the mathematical understanding and analysis of sparse grid discretization. Expand
Importance Weighted Inductive Transfer Learning for Regression
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. Expand
Analysis of Car Crash Simulation Data with Nonlinear Machine Learning Methods
This work proposes using methods from machine learning to semi-automatically analyze the arising finite element data and thereby significantly assist in the overall engineering process, and combines clustering and nonlinear dimensionality reduction to show that the method is able to automatically detect parameter dependent structure instabilities or reveal bifurcations in the time-dependent behavior of beams. Expand
Classification with sparse grids using simplicial basis functions
It turns out that the method scales linearly with the number of given data points and is well suited for data mining applications where the amount of data is very large, but where the dimension of the feature space is moderately high. Expand
On the numerical solution of the chemical master equation with sums of rank one tensors
We show that sums of rank one tensors (or separable functions) representing the so-called Candecomp/Parafac or CP-decomposition is used effectively to solve the chemical master equations as in manyExpand