Andreas Kryger Jensen

Vi Thanh Pham, Jonas Bille Nielsen, Klaus Fuglsang Kofoed et al.

The joint alignment of multivariate functional data plays an important role in various fields such as signal processing, neuroscience and medicine, including the statistical analysis of data from wearable devices. Traditional methods often ignore the phase variability and instead focus on the variability in the observed amplitude. We present a novel method for joint alignment of multivariate quasi-periodic functions using deep neural networks, decomposing, but retaining all the information in the data by preserving both phase and amplitude variability. Our proposed neural network uses a special activation of the output that builds on the unit simplex transformation, and we utilize a loss function based on the Fisher-Rao metric to train our model. Furthermore, our method is unsupervised and can provide an optimal common template function as well as subject-specific templates. We demonstrate our method on two simulated datasets and one real example, comprising data from 12-lead 10s electrocardiogram recordings.

Stéphanie M. van den Berg, Ulrich Halekoh, Sören Möller et al.

We develop a supervised deep-learning approach to estimate mutual information between two continuous random variables. As labels, we use the Linfoot informational correlation, a transformation of mutual information that has many important properties. Our method is based on ground truth labels for Gaussian and Clayton copulas. We compare our method with estimators based on kernel density, k-nearest neighbours and neural estimators. We show generally lower bias and lower variance. As a proof of principle, future research could look into training the model with a more diverse set of examples from other copulas for which ground truth labels are available.