Graph Kernels: State-of-the-Art and Future Challenges

Graph-structured data are an integral part of many application domains, including chemoinformatics, computational biology, neuroimaging, and social network analysis. Over the last two decades, numerous graph kernels, i.e. kernel functions between graphs, have been proposed to solve the problem of assessing the similarity between graphs, thereby making it possible to perform predictions in both classification and regression settings. This manuscript provides a review of existing graph kernels, their applications, software plus data resources, and an empirical comparison of state-of-the-art graph kernels.

Accelerating COVID-19 Differential Diagnosis with Explainable Ultrasound Image Analysis

Controlling the COVID-19 pandemic largely hinges upon the existence of fast, safe, and highly-available diagnostic tools. Ultrasound, in contrast to CT or X-Ray, has many practical advantages and can serve as a globally-applicable first-line examination technique. We provide the largest publicly available lung ultrasound (US) dataset for COVID-19 consisting of 106 videos from three classes (COVID-19, bacterial pneumonia, and healthy controls); curated and approved by medical experts. On this dataset, we perform an in-depth study of the value of deep learning methods for differential diagnosis of COVID-19. We propose a frame-based convolutional neural network that correctly classifies COVID-19 US videos with a sensitivity of 0.98+-0.04 and a specificity of 0.91+-08 (frame-based sensitivity 0.93+-0.05, specificity 0.87+-0.07). We further employ class activation maps for the spatio-temporal localization of pulmonary biomarkers, which we subsequently validate for human-in-the-loop scenarios in a blindfolded study with medical experts. Aiming for scalability and robustness, we perform ablation studies comparing mobile-friendly, frame- and video-based architectures and show reliability of the best model by aleatoric and epistemic uncertainty estimates. We hope to pave the road for a community effort toward an accessible, efficient and interpretable screening method and we have started to work on a clinical validation of the proposed method. Data and code are publicly available.

Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence

Functional magnetic resonance imaging (fMRI) is a crucial technology for gaining insights into cognitive processes in humans. Data amassed from fMRI measurements result in volumetric data sets that vary over time. However, analysing such data presents a challenge due to the large degree of noise and person-to-person variation in how information is represented in the brain. To address this challenge, we present a novel topological approach that encodes each time point in an fMRI data set as a persistence diagram of topological features, i.e. high-dimensional voids present in the data. This representation naturally does not rely on voxel-by-voxel correspondence and is robust towards noise. We show that these time-varying persistence diagrams can be clustered to find meaningful groupings between participants, and that they are also useful in studying within-subject brain state trajectories of subjects performing a particular task. Here, we apply both clustering and trajectory analysis techniques to a group of participants watching the movie 'Partly Cloudy'. We observe significant differences in both brain state trajectories and overall topological activity between adults and children watching the same movie.

Path Imputation Strategies for Signature Models of Irregular Time Series

The signature transform is a 'universal nonlinearity' on the space of continuous vector-valued paths, and has received attention for use in machine learning on time series. However, real-world temporal data is typically observed at discrete points in time, and must first be transformed into a continuous path before signature techniques can be applied. We make this step explicit by characterising it as an imputation problem, and empirically assess the impact of various imputation strategies when applying signature-based neural nets to irregular time series data. For one of these strategies, Gaussian process (GP) adapters, we propose an extension~(GP-PoM) that makes uncertainty information directly available to the subsequent classifier while at the same time preventing costly Monte-Carlo (MC) sampling. In our experiments, we find that the choice of imputation drastically affects shallow signature models, whereas deeper architectures are more robust. Next, we observe that uncertainty-aware predictions (based on GP-PoM or indicator imputations) are beneficial for predictive performance, even compared to the uncertainty-aware training of conventional GP adapters. In conclusion, we have demonstrated that the path construction is indeed crucial for signature models and that our proposed strategy leads to competitive performance in general, while improving robustness of signature models in particular.

Path Imputation Strategies for Signature Models

The signature transform is a 'universal nonlinearity' on the space of continuous vector-valued paths, and has received attention for use in machine learning. However real-world temporal data is typically discretised, and must first be transformed into a continuous path before signature techniques can be applied. We characterise this as an imputation problem, and empirically assess the impact of various imputation techniques when applying signatures to irregular time series data. In our experiments, we find that the choice of imputation drastically affects shallow signature models, whereas deeper architectures are more robust. We also observe that uncertainty-aware predictions are overall beneficial, even compared to the uncertainty-aware training of Gaussian process (GP) adapters. Hence, we propose an extension of GP adapters by integrating uncertainty to the prediction step. This leads to competitive performance in general, and improves robustness in signature models in particular.

Set Functions for Time Series

Despite the eminent successes of deep neural networks, many architectures are often hard to transfer to irregularly-sampled and asynchronous time series that occur in many real-world datasets, such as healthcare applications. This paper proposes a novel framework for classifying irregularly sampled time series with unaligned measurements, focusing on high scalability and data efficiency. Our method SEFT (Set Functions for Time Series) is based on recent advances in differentiable set function learning, extremely parallelizable, and scales well to very large datasets and online monitoring scenarios. We extensively compare our method to competitors on multiple healthcare time series datasets and show that it performs competitively whilst significantly reducing runtime.

Wasserstein Weisfeiler-Lehman Graph Kernels

Graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of the final set of substructures, usually a sum or average, thereby potentially discarding valuable information about the distribution of individual components. Furthermore, only a limited instance of these approaches can be extended to continuously attributed graphs. We propose a novel method that relies on the Wasserstein distance between the node feature vector distributions of two graphs, which allows to find subtler differences in data sets by considering graphs as high-dimensional objects, rather than simple means. We further propose a Weisfeiler-Lehman inspired embedding scheme for graphs with continuous node attributes and weighted edges, enhance it with the computed Wasserstein distance, and thus improve the state-of-the-art prediction performance on several graph classification tasks.

Topological Autoencoders

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we can construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded, while exhibiting favourable latent representations on synthetic manifold data sets. Moreover, on real-world data sets, introducing our topological loss leads to more meaningful latent representations while preserving low reconstruction errors.

Machine learning for early prediction of circulatory failure in the intensive care unit

Intensive care clinicians are presented with large quantities of patient information and measurements from a multitude of monitoring systems. The limited ability of humans to process such complex information hinders physicians to readily recognize and act on early signs of patient deterioration. We used machine learning to develop an early warning system for circulatory failure based on a high-resolution ICU database with 240 patient years of data. This automatic system predicts 90.0% of circulatory failure events (prevalence 3.1%), with 81.8% identified more than two hours in advance, resulting in an area under the receiver operating characteristic curve of 94.0% and area under the precision-recall curve of 63.0%. The model was externally validated in a large independent patient cohort.