The Deep Arbitrary Polynomial Chaos Neural Network or how Deep Artificial Neural Networks could benefit from Data-Driven Homogeneous Chaos Theory

no code implementations • 26 Jun 2023 • Sergey Oladyshkin, Timothy Praditia, Ilja Kröker, Farid Mohammadi, Wolfgang Nowak, Sebastian Otte

However, for a majority of deep learning approaches based on DANNs, the kernel structure of neural signal processing remains the same, where the node response is encoded as a linear superposition of neural activity, while the non-linearity is triggered by the activation functions.

A fully Bayesian sparse polynomial chaos expansion approach with joint priors on the coefficients and global selection of terms

1 code implementation • 12 Apr 2022 • Paul-Christian Bürkner, Ilja Kröker, Sergey Oladyshkin, Wolfgang Nowak

Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response surface.

Uncertainty Quantification Variable Selection