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Deep Neural Networks and PIDE discretizations
In this paper, we propose neural networks that tackle the problems of stability and field-of-view of a Convolutional Neural Network (CNN).
Explainable Machine Learning for Scientific Insights and Discoveries
Machine learning methods have been remarkably successful for a wide range of application areas in the extraction of essential information from data.
Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids
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.
A representer theorem for deep kernel learning
In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces.
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