machine-learning

Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology and physics. While it is thought that these methods preserve underlying manifold structure of data by learning a proxy for geodesic distances, no specific theoretical links have been established. Here, we establish such a link via results in Riemannian geometry explicitly connecting heat diffusion to manifold distances....

Referred to as the third rung of the causal inference ladder, counterfactual queries typically ask the" What if?" question retrospectively. The standard approach to estimate counterfactuals resides in using a structural equation model that accurately reflects the underlying data generating process. However, such models are seldom available in practice and one usually wishes to infer them from observational data alone. Unfortunately, the correct structural equation model is in general not identifiable from the observed factual distribution....

Research in Multiple Sclerosis (MS) has recently focused on extracting knowledge from real-world clinical data sources. This type of data is more abundant than data produced during clinical trials and potentially more informative about real-world clinical practice. However, this comes at the cost of less curated and controlled data sets. In this work, we address the task of optimally extracting information from longitudinal patient data in the real-world setting with a special focus on the sporadic sampling problem....

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive in terms of the Weisfeiler-Lehman graph isomorphism test. Augmenting GNNs with our layer leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets (which can be classified by humans using their topology but not by ordinary GNNs) and on real-world data....

Discovering causal structures of temporal processes is a major tool of scientific inquiry because it helps us better understand and explain the mechanisms driving a phenomenon of interest, thereby facilitating analysis, reasoning, and synthesis for such systems. However, accurately inferring causal structures within a phenomenon based on observational data only is still an open problem. Indeed, this type of data usually consists in short time series with missing or noisy values for which causal inference is increasingly difficult....