Virtual Seminar Series

Speaker: Francesco Sanna Passino, Imperial College London​

Title: On spectral embedding of dynamic multiplex graphs and subsequent inference tasks

Abstract: Many real-world networks evolve dynamically over time and present different types of connections between nodes, often called layers. In this talk, we propose and discuss a latent position model for these objects, called the dynamic multiplex random dot product graph (DMPRDPG), which uses an inner product between layer-specific and time-specific latent representations of the nodes to obtain edge probabilities. We further introduce a computationally efficient spectral embedding method for estimation of DMPRDPG parameters, called doubly unfolded adjacency spectral embedding (DUASE). The DUASE estimates are proved to be both consistent and asymptotically normally distributed. A key strength of our method is the encoding of time-specific node representations and layer-specific effects in separate latent spaces, which allows the model to capture complex behaviors while maintaining relatively low dimensionality. The embedding method we propose can also be efficiently used for subsequent inference tasks, such as clustering, anomaly detection and changepoint detection. In particular, we show how DUASE can be used to predict the response associated with an unlabeled time series of networks in a semisupervised setting, and discuss the use of DUASE for statistical hypothesis testing for differences between layers. Applications on real-world networks such as biological learning networks of larval Drosophila demonstrate practical uses of our method.​​​​​​​

Speaker: Frank Werner, University of Würzburg

Title: TBC​

Abstract: TBC​​​​​​​

Speaker: Vincent Runge,  University of Evry Paris-Saclay

Title: TBC​

Abstract: TBC​​​​​​​

Speaker: Zifeng Zhao, University of Notre Dame

Title: TBC​

Abstract: TBC​​​​​​​

Speaker: Holger Dette, Ruhr University Bochum​

Title: Multiple change point detection in functional data with applications to biomechanical fatigue data

Abstract: Injuries to the lower extremity joints are often debilitating, particularly for professional athletes. Understanding the onset of stressful conditions on these joints is therefore important in order to ensure prevention of injuries as well as individualised training for enhanced athletic performance. We study the biomechanical joint angles from the hip, knee and ankle for runners who are experiencing fatigue. The data is cyclic in nature and densely collected by body worn sensors, which makes it ideal to work with in the functional data analysis (FDA) framework. We develop a new method for multiple change point detection for functional data, which improves the state of the art  with respect to at least two  novel aspects. First, the curves are compared with respect to their maximum  absolute deviation, which leads to a better interpretation of local changes in the functional data compared to classical $L^2$-approaches. Secondly, as slight aberrations are to be often expected in a human movement data, our method will not detect arbitrarily small changes but hunts for relevant changes, where maximum absolute deviation between the curves exceeds a specified threshold, say $\Delta >0$. We recover multiple changes in a long functional time series of biomechanical knee angle data, which are larger than the desired threshold $\Delta$, allowing us to identify changes purely due to fatigue. In this work, we analyse data from both controlled indoor as well as from an uncontrolled outdoor (marathon) setting.​​​