arXiv subjects

Christopher Morris

Publications and source records attributed to Christopher Morris.

51 records · Page 3Linked to original sources

arXiv2021

The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphs

In recent years, algorithms and neural architectures based on the Weisfeiler-Leman algorithm, a well-known heuristic for the graph isomorphism problem, emerged as a powerful tool for (supervised) machine learning with graphs and relational data. Here, we give a comprehensive overview of the algorithm's use in a machine learning setting. We discuss the theoretical background, show how to use it for supervised graph- and node classification, discuss recent extensions, and its connection to neural architectures. Moreover, we give an overview of current applications and future directions to stimulate research.

cs.LG↗

arXiv2021

Temporal Graph Kernels for Classifying Dissemination Processes

Many real-world graphs or networks are temporal, e.g., in a social network persons only interact at specific points in time. This information directs dissemination processes on the network, such as the spread of rumors, fake news, or diseases. However, the current state-of-the-art methods for supervised graph classification are designed mainly for static graphs and may not be able to capture temporal information. Hence, they are not powerful enough to distinguish between graphs modeling different dissemination processes. To address this, we introduce a framework to lift standard graph kernels to the temporal domain. Specifically, we explore three different approaches and investigate the trade-offs between loss of temporal information and efficiency. Moreover, to handle large-scale graphs, we propose stochastic variants of our kernels with provable approximation guarantees. We evaluate our methods on a wide range of real-world social networks. Our methods beat static kernels by a large margin in terms of accuracy while still being scalable to large graphs and data sets. Hence, we confirm that taking temporal information into account is crucial for the successful classification of dissemination processes.

cs.SI↗

arXiv2021

Cosmic ray radiography of a human phantom

Cosmic ray muons, that reach the earth's surface, provide a natural source of radiation that is used for radiography. In this paper, we show that radiography using cosmic radiation background provides a method that can be used to monitor bulk aspects of human anatomy. We describe a method that can be used to measure changes in patients as a function of time by radiographing them using cosmic-ray muons. This could provide hourly readouts of parameters such as lung density with sufficient sensitivity to detect time changes in inflammation of the lungs in, e.g., Covid patients.

physics.med-ph↗

arXiv2020

Weisfeiler and Leman go sparse: Towards scalable higher-order graph embeddings

Graph kernels based on the $1$-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the algorithms, they might miss essential patterns in the given data and can only handle binary relations. The $k$-dimensional Weisfeiler-Leman algorithm addresses this by considering $k$-tuples, defined over the set of vertices, and defines a suitable notion of adjacency between these vertex tuples. Hence, it accounts for the higher-order interactions between vertices. However, it does not scale and may suffer from overfitting when used in a machine learning setting. Hence, it remains an important open problem to design WL-based graph learning methods that are simultaneously expressive, scalable, and non-overfitting. Here, we propose local variants and corresponding neural architectures, which consider a subset of the original neighborhood, making them more scalable, and less prone to overfitting. The expressive power of (one of) our algorithms is strictly higher than the original algorithm, in terms of ability to distinguish non-isomorphic graphs. Our experimental study confirms that the local algorithms, both kernel and neural architectures, lead to vastly reduced computation times, and prevent overfitting. The kernel version establishes a new state-of-the-art for graph classification on a wide range of benchmark datasets, while the neural version shows promising performance on large-scale molecular regression tasks.

cs.DS↗

arXiv2020

TUDataset: A collection of benchmark datasets for learning with graphs

Recently, there has been an increasing interest in (supervised) learning with graph data, especially using graph neural networks. However, the development of meaningful benchmark datasets and standardized evaluation procedures is lagging, consequently hindering advancements in this area. To address this, we introduce the TUDataset for graph classification and regression. The collection consists of over 120 datasets of varying sizes from a wide range of applications. We provide Python-based data loaders, kernel and graph neural network baseline implementations, and evaluation tools. Here, we give an overview of the datasets, standardized evaluation procedures, and provide baseline experiments. All datasets are available at www.graphlearning.io. The experiments are fully reproducible from the code available at www.github.com/chrsmrrs/tudataset.

cs.LG↗

arXiv2020

A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification.

cs.LG↗

arXiv2020

Deep Graph Matching Consensus

This work presents a two-stage neural architecture for learning and refining structural correspondences between graphs. First, we use localized node embeddings computed by a graph neural network to obtain an initial ranking of soft correspondences between nodes. Secondly, we employ synchronous message passing networks to iteratively re-rank the soft correspondences to reach a matching consensus in local neighborhoods between graphs. We show, theoretically and empirically, that our message passing scheme computes a well-founded measure of consensus for corresponding neighborhoods, which is then used to guide the iterative re-ranking process. Our purely local and sparsity-aware architecture scales well to large, real-world inputs while still being able to recover global correspondences consistently. We demonstrate the practical effectiveness of our method on real-world tasks from the fields of computer vision and entity alignment between knowledge graphs, on which we improve upon the current state-of-the-art. Our source code is available under https://github.com/rusty1s/ deep-graph-matching-consensus.

cs.LG↗

arXiv2019

A Unifying View of Explicit and Implicit Feature Maps of Graph Kernels

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact and approximative feature maps for widely used graph kernels based on the kernel trick. We analyze for which kernels and graph properties computation by explicit feature maps is feasible and actually more efficient. In particular, we derive approximative, explicit feature maps for state-of-the-art kernels supporting real-valued attributes including the GraphHopper and graph invariant kernels. In extensive experiments we show that our approaches often achieve a classification accuracy close to the exact methods based on the kernel trick, but require only a fraction of their running time. Moreover, we propose and analyze algorithms for computing random walk, shortest-path and subgraph matching kernels by explicit and implicit feature maps. Our theoretical results are confirmed experimentally by observing a phase transition when comparing running time with respect to label diversity, walk lengths and subgraph size, respectively.

cs.LG↗

arXiv2019

Hierarchical Graph Representation Learning with Differentiable Pooling

Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.

cs.LG↗

arXiv2018

3D Cosmic Ray Muon Tomography from an Underground Tunnel

We present an underground cosmic ray muon tomographic experiment imaging 3D density of overburden, part of a joint study with differential gravity. Muon data were acquired at four locations within a tunnel beneath Los Alamos, New Mexico, and used in a 3D tomographic inversion to recover the spatial variation in the overlying rock-air interface, and compared with a priori knowledge of the topography. Densities obtained exhibit good agreement with preliminary results of the gravity modeling, which will be presented elsewhere, and are compatible with values reported in the literature. The modeled rock-air interface matches that obtained from LIDAR within 4 m, our resolution, over much of the model volume. This experiment demonstrates the power of cosmic ray muons to image shallow geological targets using underground detectors, whose development as borehole devices will be an important new direction of passive geophysical imaging.

physics.geo-ph↗

arXiv2017

Global Weisfeiler-Lehman Graph Kernels

Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take global graph propertiesinto account may not scale well to large graph databases. Here we propose to start exploring the space between local and global graph kernels, striking the balance between both worlds. Specifically, we introduce a novel graph kernel based on the $k$-dimensional Weisfeiler-Lehman algorithm. Unfortunately, the $k$-dimensional Weisfeiler-Lehman algorithm scales exponentially in $k$. Consequently, we devise a stochastic version of the kernel with provable approximation guarantees using conditional Rademacher averages. On bounded-degree graphs, it can even be computed in constant time. We support our theoretical results with experiments on several graph classification benchmarks, showing that our kernels often outperform the state-of-the-art in terms of classification accuracies.

cs.LG↗

arXiv2016

Output-sensitive Complexity of Multiobjective Combinatorial Optimization

We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is output-sensitive, i.e., its running time is bounded by a polynomial in the input and the output size. We provide both practical examples of MOCO problems for which such an efficient algorithm exists as well as problems for which no efficient algorithm exists under mild complexity theoretic assumptions.

math.OC↗

arXiv2016

Faster Kernels for Graphs with Continuous Attributes via Hashing

While state-of-the-art kernels for graphs with discrete labels scale well to graphs with thousands of nodes, the few existing kernels for graphs with continuous attributes, unfortunately, do not scale well. To overcome this limitation, we present hash graph kernels, a general framework to derive kernels for graphs with continuous attributes from discrete ones. The idea is to iteratively turn continuous attributes into discrete labels using randomized hash functions. We illustrate hash graph kernels for the Weisfeiler-Lehman subtree kernel and for the shortest-path kernel. The resulting novel graph kernels are shown to be, both, able to handle graphs with continuous attributes and scalable to large graphs and data sets. This is supported by our theoretical analysis and demonstrated by an extensive experimental evaluation.

cs.LG↗

arXiv2012

Obtaining material identification with cosmic ray radiography

The passage of muons through matter is mostly affected by their Coulomb interactions with electrons and nuclei. The muon interactions with electrons lead to continuous energy loss and stopping of muons, while their scattering off nuclei lead to angular 'diffusion'. By measuring both the number of stopped muons and angular changes in muon trajectories we can estimate density and identify materials. Here we demonstrate the material identification using data taken at Los Alamos with the Mini Muon Tracker.

physics.ins-det↗

arXiv2012

Cosmic Ray Radiography of the Damaged Cores of the Fukushima Reactors

The passage of muons through matter is dominated by the Coulomb interaction with electrons and nuclei. The interaction with the electrons leads to continuous energy loss and stopping of the muons. The interaction with nuclei leads to angle diffusion. Two muon imaging methods that use flux attenuation and multiple Coulomb scattering of cosmic-ray muons are being studied as tools for diagnosing the damaged cores of the Fukushima reactors. Here we compare these two methods. We conclude that the scattering method can provide detailed information about the core. Attenuation has low contrast and little sensitivity to the core.

physics.ins-det↗