Variable Transformations in combination with Wavelets and ANOVA for high-dimensional approximation

Understand

We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions.

• Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus.
• With a variable transformation we are able to transform the approximation rates and fast algorithms from the torus to other domains.
• We perform and analyze scattered-data approximation for smooth but arbitrary density functions by using a least squares method.