Aleksandar Bojchevski, Stephan Günnemann
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on large scale (attributed) graphs that show strong performance on tasks such as link prediction and node classification. Unlike most approaches that represent nodes as point vectors in a low-dimensional continuous space, we embed each node as a Gaussian distribution, allowing us to capture uncertainty about the representation. Furthermore, we propose an unsupervised method that handles inductive learning scenarios and is applicable to different types of graphs: plain/attributed, directed/undirected. By leveraging both the network structure and the associated node attributes, we are able to generalize to unseen nodes without additional training. To learn the embeddings we adopt a personalized ranking formulation w.r.t. the node distances that exploits the natural ordering of the nodes imposed by the network structure. Experiments on real world networks demonstrate the high performance of our approach, outperforming state-of-the-art network embedding methods on several different tasks. Additionally, we demonstrate the benefits of modeling uncertainty - by analyzing it we can estimate neighborhood diversity and detect the intrinsic latent dimensionality of a graph.
Aleksandar Bojchevski, Oleksandr Shchur, Daniel Zügner, Stephan Günnemann
We propose NetGAN - the first implicit generative model for graphs able to mimic real-world networks. We pose the problem of graph generation as learning the distribution of biased random walks over the input graph. The proposed model is based on a stochastic neural network that generates discrete output samples and is trained using the Wasserstein GAN objective. NetGAN is able to produce graphs that exhibit well-known network patterns without explicitly specifying them in the model definition. At the same time, our model exhibits strong generalization properties, as highlighted by its competitive link prediction performance, despite not being trained specifically for this task. Being the first approach to combine both of these desirable properties, NetGAN opens exciting avenues for further research.
Wolfgang Gatterbauer, Stephan Günnemann, Danai Koutra, Christos Faloutsos
How can we tell when accounts are fake or real in a social network? And how can we tell which accounts belong to liberal, conservative or centrist users? Often, we can answer such questions and label nodes in a network based on the labels of their neighbors and appropriate assumptions of homophily ("birds of a feather flock together") or heterophily ("opposites attract"). One of the most widely used methods for this kind of inference is Belief Propagation (BP) which iteratively propagates the information from a few nodes with explicit labels throughout a network until convergence. One main problem with BP, however, is that there are no known exact guarantees of convergence in graphs with loops. This paper introduces Linearized Belief Propagation (LinBP), a linearization of BP that allows a closed-form solution via intuitive matrix equations and, thus, comes with convergence guarantees. It handles homophily, heterophily, and more general cases that arise in multi-class settings. Plus, it allows a compact implementation in SQL. The paper also introduces Single-pass Belief Propagation (SBP), a "localized" version of LinBP that propagates information across every edge at most once and for which the final class assignments depend only on the nearest labeled neighbors. In addition, SBP allows fast incremental updates in dynamic networks. Our runtime experiments show that LinBP and SBP are orders of magnitude faster than standard
Stephan Günnemann, Hardy Kremer, Matthias Hannen, Thomas Seidl
Analyzing high dimensional data is a challenging task. For these data it is known that traditional clustering algorithms fail to detect meaningful patterns. As a solution, subspace clustering techniques have been introduced. They analyze arbitrary subspace projections of the data to detect clustering structures. In this paper, we present our subspace clustering extension for KDD frameworks, termed KDD-SC. In contrast to existing subspace clustering toolkits, our solution neither is a standalone product nor is it tightly coupled to a specific KDD framework. Our extension is realized by a common codebase and easy-to-use plugins for three of the most popular KDD frameworks, namely KNIME, RapidMiner, and WEKA. KDD-SC extends these frameworks such that they offer a wide range of different subspace clustering functionalities. It provides a multitude of algorithms, data generators, evaluation measures, and visualization techniques specifically designed for subspace clustering. These functionalities integrate seamlessly with the frameworks' existing features such that they can be flexibly combined. KDD-SC is publicly available on our website.
Stephan Rabanser, Oleksandr Shchur, Stephan Günnemann
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to numerous other disciplines, including machine learning. Tensors and their decompositions are especially beneficial in unsupervised learning settings, but are gaining popularity in other sub-disciplines like temporal and multi-relational data analysis, too. The scope of this paper is to give a broad overview of tensors, their decompositions, and how they are used in machine learning. As part of this, we are going to introduce basic tensor concepts, discuss why tensors can be considered more rigid than matrices with respect to the uniqueness of their decomposition, explain the most important factorization algorithms and their properties, provide concrete examples of tensor decomposition applications in machine learning, conduct a case study on tensor-based estimation of mixture models, talk about the current state of research, and provide references to available software libraries.
Saskia Metzler, Stephan Günnemann, Pauli Miettinen
Cliques are frequently used to model communities: a community is a set of nodes where each pair is equally likely to be connected. But studying real-world communities reveals that they have more structure than that. In particular, the nodes can be ordered in such a way that (almost) all edges in the community lie below a hyperbola. In this paper we present three new models for communities that capture this phenomenon. Our models explain the structure of the communities differently, but we also prove that they are identical in their expressive power. Our models fit to real-world data much better than traditional block models or previously-proposed hyperbolic models, both of which are a special case of our model. Our models also allow for intuitive interpretation of the parameters, enabling us to summarize the shapes of the communities in graphs effectively.
Bryan Hooi, Neil Shah, Alex Beutel, Stephan Gunnemann, Leman Akoglu, Mohit Kumar, Disha Makhija, Christos Faloutsos
Review fraud is a pervasive problem in online commerce, in which fraudulent sellers write or purchase fake reviews to manipulate perception of their products and services. Fake reviews are often detected based on several signs, including 1) they occur in short bursts of time; 2) fraudulent user accounts have skewed rating distributions. However, these may both be true in any given dataset. Hence, in this paper, we propose an approach for detecting fraudulent reviews which combines these 2 approaches in a principled manner, allowing successful detection even when one of these signs is not present. To combine these 2 approaches, we formulate our Bayesian Inference for Rating Data (BIRD) model, a flexible Bayesian model of user rating behavior. Based on our model we formulate a likelihood-based suspiciousness metric, Normalized Expected Surprise Total (NEST). We propose a linear-time algorithm for performing Bayesian inference using our model and computing the metric. Experiments on real data show that BIRDNEST successfully spots review fraud in large, real-world graphs: the 50 most suspicious users of the Flipkart platform flagged by our algorithm were investigated and all identified as fraudulent by domain experts at Flipkart.
Nick Harmening, Marin Biloš, Stephan Günnemann
Determining the traffic scenario space is a major challenge for the homologation and coverage assessment of automated driving functions. In contrast to current approaches that are mainly scenario-based and rely on expert knowledge, we introduce two data driven autoencoding models that learn a latent representation of traffic scenes. First is a CNN based spatio-temporal model that autoencodes a grid of traffic participants' positions. Secondly, we develop a pure temporal RNN based model that auto-encodes a sequence of sets. To handle the unordered set data, we had to incorporate the permutation invariance property. Finally, we show how the latent scenario embeddings can be used for clustering traffic scenarios and similarity retrieval.
Aleksandar Bojchevski, Stephan Günnemann
Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks on both the graph structure and the node attributes. We propose the first method for verifying certifiable (non-)robustness to graph perturbations for a general class of models that includes graph neural networks and label/feature propagation. By exploiting connections to PageRank and Markov decision processes our certificates can be efficiently (and under many threat models exactly) computed. Furthermore, we investigate robust training procedures that increase the number of certifiably robust nodes while maintaining or improving the clean predictive accuracy.
Sebastian Schmidt, Stephan Günnemann
Active learning (AL) reduces the amount of labeled data needed to train a machine learning model by intelligently choosing which instances to label. Classic pool-based AL requires all data to be present in a datacenter, which can be challenging with the increasing amounts of data needed in deep learning. However, AL on mobile devices and robots, like autonomous cars, can filter the data from perception sensor streams before reaching the datacenter. We exploited the temporal properties for such image streams in our work and proposed the novel temporal predicted loss (TPL) method. To evaluate the stream-based setting properly, we introduced the GTA V streets and the A2D2 streets dataset and made both publicly available. Our experiments showed that our approach significantly improves the diversity of the selection while being an uncertainty-based method. As pool-based approaches are more common in perception applications, we derived a concept for comparing pool-based and stream-based AL, where TPL out-performed state-of-the-art pool- or stream-based approaches for different models. TPL demonstrated a gain of 2.5 precept points (pp) less required data while being significantly faster than pool-based methods.
Jianxiang Feng, Jongseok Lee, Simon Geisler, Stephan Gunnemann, Rudolph Triebel
To facilitate reliable deployments of autonomous robots in the real world, Out-of-Distribution (OOD) detection capabilities are often required. A powerful approach for OOD detection is based on density estimation with Normalizing Flows (NFs). However, we find that prior work with NFs attempts to match the complex target distribution topologically with naive base distributions leading to adverse implications. In this work, we circumvent this topological mismatch using an expressive class-conditional base distribution trained with an information-theoretic objective to match the required topology. The proposed method enjoys the merits of wide compatibility with existing learned models without any performance degradation and minimum computation overhead while enhancing OOD detection capabilities. We demonstrate superior results in density estimation and 2D object detection benchmarks in comparison with extensive baselines. Moreover, we showcase the applicability of the method with a real-robot deployment.
Raffaele Paolino, Aleksandar Bojchevski, Stephan Günnemann, Gitta Kutyniok, Ron Levie
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius. Currently, the literature mostly focuses on uniform sampling and constant neighborhood radius. However, real-world graphs are likely to be better represented by a model in which the sampling density and the neighborhood radius can both vary over the latent space. For instance, in a social network communities can be modeled as densely sampled areas, and hubs as nodes with larger neighborhood radius. In this work, we first perform a rigorous mathematical analysis of this (more general) class of models, including derivations of the resulting graph shift operators. The key insight is that graph shift operators should be corrected in order to avoid potential distortions introduced by the non-uniform sampling. Then, we develop methods to estimate the unknown sampling density in a self-supervised fashion. Finally, we present exemplary applications in which the learnt density is used to 1) correct the graph shift operator and improve performance on a variety of tasks, 2) improve pooling, and 3) extract knowledge from networks. Our experimental findings support our theory and provide strong evidence for our model.
Johannes Gasteiger, Chendi Qian, Stephan Günnemann
Using graph neural networks for large graphs is challenging since there is no clear way of constructing mini-batches. To solve this, previous methods have relied on sampling or graph clustering. While these approaches often lead to good training convergence, they introduce significant overhead due to expensive random data accesses and perform poorly during inference. In this work we instead focus on model behavior during inference. We theoretically model batch construction via maximizing the influence score of nodes on the outputs. This formulation leads to optimal approximation of the output when we do not have knowledge of the trained model. We call the resulting method influence-based mini-batching (IBMB). IBMB accelerates inference by up to 130x compared to previous methods that reach similar accuracy. Remarkably, with adaptive optimization and the right training schedule IBMB can also substantially accelerate training, thanks to precomputed batches and consecutive memory accesses. This results in up to 18x faster training per epoch and up to 17x faster convergence per runtime compared to previous methods.
Jan Schuchardt, Aleksandar Bojchevski, Johannes Gasteiger, Stephan Günnemann
In tasks like node classification, image segmentation, and named-entity recognition we have a classifier that simultaneously outputs multiple predictions (a vector of labels) based on a single input, i.e. a single graph, image, or document respectively. Existing adversarial robustness certificates consider each prediction independently and are thus overly pessimistic for such tasks. They implicitly assume that an adversary can use different perturbed inputs to attack different predictions, ignoring the fact that we have a single shared input. We propose the first collective robustness certificate which computes the number of predictions that are simultaneously guaranteed to remain stable under perturbation, i.e. cannot be attacked. We focus on Graph Neural Networks and leverage their locality property - perturbations only affect the predictions in a close neighborhood - to fuse multiple single-node certificates into a drastically stronger collective certificate. For example, on the Citeseer dataset our collective certificate for node classification increases the average number of certifiable feature perturbations from $7$ to $351$.
Tom Wollschläger, Nicholas Gao, Bertrand Charpentier, Mohamed Amine Ketata, Stephan Günnemann
Graph Neural Networks (GNNs) are promising surrogates for quantum mechanical calculations as they establish unprecedented low errors on collections of molecular dynamics (MD) trajectories. Thanks to their fast inference times they promise to accelerate computational chemistry applications. Unfortunately, despite low in-distribution (ID) errors, such GNNs might be horribly wrong for out-of-distribution (OOD) samples. Uncertainty estimation (UE) may aid in such situations by communicating the model's certainty about its prediction. Here, we take a closer look at the problem and identify six key desiderata for UE in molecular force fields, three 'physics-informed' and three 'application-focused' ones. To overview the field, we survey existing methods from the field of UE and analyze how they fit to the set desiderata. By our analysis, we conclude that none of the previous works satisfies all criteria. To fill this gap, we propose Localized Neural Kernel (LNK) a Gaussian Process (GP)-based extension to existing GNNs satisfying the desiderata. In our extensive experimental evaluation, we test four different UE with three different backbones and two datasets. In out-of-equilibrium detection, we find LNK yielding up to 2.5 and 2.1 times lower errors in terms of AUC-ROC score than dropout or evidential regression-based methods while maintaining high predictive performance.
Johanna Sommer, Leon Hetzel, David Lüdke, Fabian Theis, Stephan Günnemann
Machine learning for molecules holds great potential for efficiently exploring the vast chemical space and thus streamlining the drug discovery process by facilitating the design of new therapeutic molecules. Deep generative models have shown promising results for molecule generation, but the benefits of specific inductive biases for learning distributions over small graphs are unclear. Our study aims to investigate the impact of subgraph structures and vocabulary design on distribution learning, using small drug molecules as a case study. To this end, we introduce Subcover, a new subgraph-based fragmentation scheme, and evaluate it through a two-step variational auto-encoder. Our results show that Subcover's improved identification of chemically meaningful subgraphs leads to a relative improvement of the FCD score by 30%, outperforming previous methods. Our findings highlight the potential of Subcover to enhance the performance and scalability of existing methods, contributing to the advancement of drug discovery.
Anna-Kathrin Kopetzki, Stephan Günnemann
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and reliability of predictions. We answer these questions by computing reachable sets of neural networks, i.e. sets of outputs resulting from continuous sets of inputs. We provide two efficient approaches that lead to over- and under-approximations of the reachable set. This principle is highly versatile, as we show. First, we use it to analyze and enhance the robustness properties of both classifiers and regression models. This is in contrast to existing works, which are mainly focused on classification. Specifically, we verify (non-)robustness, propose a robust training procedure, and show that our approach outperforms adversarial attacks as well as state-of-the-art methods of verifying classifiers for non-norm bound perturbations. Second, we provide techniques to distinguish between reliable and non-reliable predictions for unlabeled inputs, to quantify the influence of each feature on a prediction, and compute a feature ranking.
Johannes Gasteiger, Aleksandar Bojchevski, Stephan Günnemann
Neural message passing algorithms for semi-supervised classification on graphs have recently achieved great success. However, for classifying a node these methods only consider nodes that are a few propagation steps away and the size of this utilized neighborhood is hard to extend. In this paper, we use the relationship between graph convolutional networks (GCN) and PageRank to derive an improved propagation scheme based on personalized PageRank. We utilize this propagation procedure to construct a simple model, personalized propagation of neural predictions (PPNP), and its fast approximation, APPNP. Our model's training time is on par or faster and its number of parameters on par or lower than previous models. It leverages a large, adjustable neighborhood for classification and can be easily combined with any neural network. We show that this model outperforms several recently proposed methods for semi-supervised classification in the most thorough study done so far for GCN-like models. Our implementation is available online.
Armin Moin, Andrei Mituca, Moharram Challenger, Atta Badii, Stephan Günnemann
In this paper, we present ML-Quadrat, an open-source research prototype that is based on the Eclipse Modeling Framework (EMF) and the state of the art in the literature of Model-Driven Software Engineering (MDSE) for smart Cyber-Physical Systems (CPS) and the Internet of Things (IoT). Its envisioned users are mostly software developers who might not have deep knowledge and skills in the heterogeneous IoT platforms and the diverse Artificial Intelligence (AI) technologies, specifically regarding Machine Learning (ML). ML-Quadrat is released under the terms of the Apache 2.0 license on Github. Additionally, we demonstrate an early tool prototype of DriotData, a web-based Low-Code platform targeting citizen data scientists and citizen/end-user software developers. DriotData exploits and adopts ML-Quadrat in the industry by offering an extended version of it as a subscription-based service to companies, mainly Small- and Medium-Sized Enterprises (SME). The current preliminary version of DriotData has three web-based model editors: text-based, tree-/form-based and diagram-based. The latter is designed for domain experts in the problem or use case domains (namely the IoT vertical domains) who might not have knowledge and skills in the field of IT. Finally, a short video demonstrating the tools is available on YouTube: https://youtu.be/VAuz25w0a5k
Oleksandr Shchur, Stephan Günnemann
Community detection is a fundamental problem in machine learning. While deep learning has shown great promise in many graphrelated tasks, developing neural models for community detection has received surprisingly little attention. The few existing approaches focus on detecting disjoint communities, even though communities in real graphs are well known to be overlapping. We address this shortcoming and propose a graph neural network (GNN) based model for overlapping community detection. Despite its simplicity, our model outperforms the existing baselines by a large margin in the task of community recovery. We establish through an extensive experimental evaluation that the proposed model is effective, scalable and robust to hyperparameter settings. We also perform an ablation study that confirms that GNN is the key ingredient to the power of the proposed model.