Online topology estimation of graph-connected time series is challenging in practice, particularly because the dependencies between the time series in many real-world scenarios are nonlinear. To address this challenge, we introduce a novel kernel-based algorithm for online graph topology estimation. Our proposed algorithm also performs a Fourier-based random feature approximation to tackle the curse of dimensionality associated with kernel representations. Exploiting the fact that real-world networks often exhibit sparse topologies, we propose a group-Lasso based optimization framework, which is solved using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. We provide theoretical guarantees for our algorithm and prove that it can achieve sublinear dynamic regret under certain reasonable assumptions. In experiments conducted on both real and synthetic data, our method outperforms existing state-of-the-art competitors.

Deep neural networks are complex machine learning models that have shown promising results in analyzing high-dimensional data such as those collected from medical examinations. Such models have the potential to provide fast and accurate medical diagnoses. However, the high complexity makes deep neural networks and their predictions difficult to understand. Providing model explanations can be a way of increasing the understanding of “black box” models and building trust. In this work, we applied transfer learning to develop a deep neural network to predict sex from electrocardiograms. Using the visual explanation method Grad-CAM, heat maps were generated from the model in order to understand how it makes predictions. To evaluate the usefulness of the heat maps and determine if the heat maps identified electrocardiogram features that could be recognized to discriminate sex, medical doctors provided feedback. Based on the feedback, we concluded that, in our setting, this mode of explainable artificial intelligence does not provide meaningful information to medical doctors and is not useful in the clinic. Our results indicate that improved explanation techniques that are tailored to medical data should be developed before deep neural networks can be applied in the clinic for diagnostic purposes.