For a d-ary Boolean function Φ: {0, 1}^d → {0, 1} and an assignment to its variables x = (x₁, x₂, . . . , x_d) we consider the problem of finding those subsets of the variables that are sufficient to determine the function value with a given probability δ. This is motivated by the task of interpreting predictions of binary classifiers described as Boolean ...

We perform a comprehensive numerical study of the effect of approximation-theoretical results for neural networks on practical learning problems in the context of numerical analysis. As the underlying model, we study the machine-learning-based solution of parametric partial differential equations. Here, approximation theory for fully-connected neural networks predicts that the performance of the ...

Global Navigation Satellite Systems typically perform poorly in urban environments, where the likelihood of line-of-sight conditions between devices and satellites is low. Therefore, alternative location methods are required to achieve good accuracy. We present LocUNet: A convolutional, end-to-end trained neural network (NN) for the localization task, which is able to estimate the position of a user ...

We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent low dimensionality of the solution manifold to obtain approximation rates which are significantly superior to those provided by classical neural network approximation results. ...

Methods for electro- or magnetoencephalography (EEG/MEG) based brain source imaging (BSI) using sparse Bayesian learning (SBL) have been demonstrated to achieve excellent performance in situations with low numbers of distinct active sources, such as event-related designs. This paper extends the theory and practice of SBL in three important ways. First, we reformulate three existing SBL algorithms ...