11 accepted papers
We investigate the trade-off between expressive power and privacy guarantees in graph representation learning. Privacy-preserving machine learning faces growing regulatory demands that pose a fundamental challenge: safeguarding sensitive data while maintaining expressive power. To address this chall…
We propose and investigate probabilistic guarantees for the adversarial robustness of classification algorithms. While traditional formal verification approaches for robustness are intractable and sampling-based approaches do not provide formal guarantees, our approach is able to efficiently certify…
We investigate the distance function learned by message passing neural networks (MPNNs) in specific tasks, aiming to capture the _functional_ distance between prediction targets that MPNNs implicitly learn. This contrasts with previous work, which links MPNN distances on arbitrary tasks to _structu…
We systematically investigate the expressive power of path-based graph neural networks. While it has been shown that path-based graph neural networks can achieve strong empirical results, an investigation into their expressive power is lacking. Therefore, we propose PATH-WL, a general class of color…
We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently fo…
We systematically investigate graph transformations that enable standard message passing to simulate state-of-the-art graph neural networks (GNNs) without loss of expressivity. Using these, many state-of-the-art GNNs can be implemented with message passing operations from standard libraries, elimina…
We systematically study the query complexity of learning geodesically convex halfspaces on graphs. Geodesic convexity is a natural generalisation of Euclidean convexity and allows the definition of convex sets and halfspaces on graphs. We prove an upper bound on the query complexity linear in the tr…
We provide the first mathematically complete derivation of the Nystr{ö}m method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building on this result, we devise highly scalable methods for learn…
We present a novel parallelisation scheme that simplifies the adaptation of learning algorithms to growing amounts of data as well as growing needs for accurate and confident predictions in critical applications. In contrast to other parallelisation techniques, it can be applied to a broad class of…
We investigate, theoretically and empirically, the effectiveness of kernel K-means++ samples as landmarks in the Nyström method for low-rank approximation of kernel matrices. Previous empirical studies (Zhang et al., 2008; Kumar et al.,2012) observe that the landmarks obtained using (kernel) K-means…
We present an effective method for supervised feature construction. The main goal of the approach is to construct a feature representation for which a set of linear hypotheses is of sufficient capacity -- large enough to contain a satisfactory solution to the considered problem and small enough to a…