Distilling Influences to Mitigate Prediction Churn in Graph Neural Networks

Models with similar performances exhibit significant disagreement in the predictions of individual samples, referred to as prediction churn. Our work explores this phenomenon in graph neural networks by investigating differences between models differing only in their initializations in their utilized features for predictions. We propose a novel metric called Influence Difference (ID) to quantify the variation in reasons used by nodes across models by comparing their influence distribution. Additionally, we consider the differences between nodes with a stable and an unstable prediction, positing that both equally utilize different reasons and thus provide a meaningful gradient signal to closely match two models even when the predictions for nodes are similar. Based on our analysis, we propose to minimize this ID in Knowledge Distillation, a domain where a new model should closely match an established one. As an efficient approximation, we introduce DropDistillation (DD) that matches the output for a graph perturbed by edge deletions. Our empirical evaluation of six benchmark datasets for node classification validates the differences in utilized features. DD outperforms previous methods regarding prediction stability and overall performance in all considered Knowledge Distillation experiments.

Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networks

Our study reveals new theoretical insights into over-smoothing and feature over-correlation in deep graph neural networks. We show the prevalence of invariant subspaces, demonstrating a fixed relative behavior that is unaffected by feature transformations. Our work clarifies recent observations related to convergence to a constant state and a potential over-separation of node states, as the amplification of subspaces only depends on the spectrum of the aggregation function. In linear scenarios, this leads to node representations being dominated by a low-dimensional subspace with an asymptotic convergence rate independent of the feature transformations. This causes a rank collapse of the node representations, resulting in over-smoothing when smooth vectors span this subspace, and over-correlation even when over-smoothing is avoided. Guided by our theory, we propose a sum of Kronecker products as a beneficial property that can provably prevent over-smoothing, over-correlation, and rank collapse. We empirically extend our insights to the non-linear case, demonstrating the inability of existing models to capture linearly independent features.

Curvature-based Pooling within Graph Neural Networks

Over-squashing and over-smoothing are two critical issues, that limit the capabilities of graph neural networks (GNNs). While over-smoothing eliminates the differences between nodes making them indistinguishable, over-squashing refers to the inability of GNNs to propagate information over long distances, as exponentially many node states are squashed into fixed-size representations. Both phenomena share similar causes, as both are largely induced by the graph topology. To mitigate these problems in graph classification tasks, we propose CurvPool, a novel pooling method. CurvPool exploits the notion of curvature of a graph to adaptively identify structures responsible for both over-smoothing and over-squashing. By clustering nodes based on the Balanced Forman curvature, CurvPool constructs a graph with a more suitable structure, allowing deeper models and the combination of distant information. We compare it to other state-of-the-art pooling approaches and establish its competitiveness in terms of classification accuracy, computational complexity, and flexibility. CurvPool outperforms several comparable methods across all considered tasks. The most consistent results are achieved by pooling densely connected clusters using the sum aggregation, as this allows additional information about the size of each pool.

Distributed LSTM-Learning from Differentially Private Label Proportions

Data privacy and decentralised data collection has become more and more popular in recent years. In order to solve issues with privacy, communication bandwidth and learning from spatio-temporal data, we will propose two efficient models which use Differential Privacy and decentralized LSTM-Learning: One, in which a Long Short Term Memory (LSTM) model is learned for extracting local temporal node constraints and feeding them into a Dense-Layer (LabelProportionToLocal). The other approach extends the first one by fetching histogram data from the neighbors and joining the information with the LSTM output (LabelProportionToDense). For evaluation two popular datasets are used: Pems-Bay and METR-LA. Additionally, we provide an own dataset, which is based on LuST. The evaluation will show the tradeoff between performance and data privacy.

LOSDD: Leave-Out Support Vector Data Description for Outlier Detection

Support Vector Machines have been successfully used for one-class classification (OCSVM, SVDD) when trained on clean data, but they work much worse on dirty data: outliers present in the training data tend to become support vectors, and are hence considered "normal". In this article, we improve the effectiveness to detect outliers in dirty training data with a leave-out strategy: by temporarily omitting one candidate at a time, this point can be judged using the remaining data only. We show that this is more effective at scoring the outlierness of points than using the slack term of existing SVM-based approaches. Identified outliers can then be removed from the data, such that outliers hidden by other outliers can be identified, to reduce the problem of masking. Naively, this approach would require training N individual SVMs (and training $O(N^2)$ SVMs when iteratively removing the worst outliers one at a time), which is prohibitively expensive. We will discuss that only support vectors need to be considered in each step and that by reusing SVM parameters and weights, this incremental retraining can be accelerated substantially. By removing candidates in batches, we can further improve the processing time, although it obviously remains more costly than training a single SVM.

Forecasting Unobserved Node States with spatio-temporal Graph Neural Networks

Forecasting future states of sensors is key to solving tasks like weather prediction, route planning, and many others when dealing with networks of sensors. But complete spatial coverage of sensors is generally unavailable and would practically be infeasible due to limitations in budget and other resources during deployment and maintenance. Currently existing approaches using machine learning are limited to the spatial locations where data was observed, causing limitations to downstream tasks. Inspired by the recent surge of Graph Neural Networks for spatio-temporal data processing, we investigate whether these can also forecast the state of locations with no sensors available. For this purpose, we develop a framework, named Forecasting Unobserved Node States (FUNS), that allows forecasting the state at entirely unobserved locations based on spatio-temporal correlations and the graph inductive bias. FUNS serves as a blueprint for optimizing models only on observed data and demonstrates good generalization capabilities for predicting the state at entirely unobserved locations during the testing stage. Our framework can be combined with any spatio-temporal Graph Neural Network, that exploits spatio-temporal correlations with surrounding observed locations by using the network's graph structure. Our employed model builds on a previous model by also allowing us to exploit prior knowledge about locations of interest, e.g. the road type. Our empirical evaluation of both simulated and real-world datasets demonstrates that Graph Neural Networks are well-suited for this task.

Certified Data Removal in Sum-Product Networks

Data protection regulations like the GDPR or the California Consumer Privacy Act give users more control over the data that is collected about them. Deleting the collected data is often insufficient to guarantee data privacy since it is often used to train machine learning models, which can expose information about the training data. Thus, a guarantee that a trained model does not expose information about its training data is additionally needed. In this paper, we present UnlearnSPN -- an algorithm that removes the influence of single data points from a trained sum-product network and thereby allows fulfilling data privacy requirements on demand.

Evaluating Machine Unlearning via Epistemic Uncertainty

There has been a growing interest in Machine Unlearning recently, primarily due to legal requirements such as the General Data Protection Regulation (GDPR) and the California Consumer Privacy Act. Thus, multiple approaches were presented to remove the influence of specific target data points from a trained model. However, when evaluating the success of unlearning, current approaches either use adversarial attacks or compare their results to the optimal solution, which usually incorporates retraining from scratch. We argue that both ways are insufficient in practice. In this work, we present an evaluation metric for Machine Unlearning algorithms based on epistemic uncertainty. This is the first definition of a general evaluation metric for Machine Unlearning to our best knowledge.

Transforming PageRank into an Infinite-Depth Graph Neural Network

Popular graph neural networks are shallow models, despite the success of very deep architectures in other application domains of deep learning. This reduces the modeling capacity and leaves models unable to capture long-range relationships. The primary reason for the shallow design results from over-smoothing, which leads node states to become more similar with increased depth. We build on the close connection between GNNs and PageRank, for which personalized PageRank introduces the consideration of a personalization vector. Adopting this idea, we propose the Personalized PageRank Graph Neural Network (PPRGNN), which extends the graph convolutional network to an infinite-depth model that has a chance to reset the neighbor aggregation back to the initial state in each iteration. We introduce a nicely interpretable tweak to the chance of resetting and prove the convergence of our approach to a unique solution without placing any constraints, even when taking infinitely many neighbor aggregations. As in personalized PageRank, our result does not suffer from over-smoothing. While doing so, time complexity remains linear while we keep memory complexity constant, independently of the depth of the network, making it scale well to large graphs. We empirically show the effectiveness of our approach for various node and graph classification tasks. PPRGNN outperforms comparable methods in almost all cases.

Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures

Bayesian networks are a central tool in machine learning and artificial intelligence, and make use of conditional independencies to impose structure on joint distributions. However, they are generally not as expressive as deep learning models and inference is hard and slow. In contrast, deep probabilistic models such as sum-product networks (SPNs) capture joint distributions in a tractable fashion, but use little interpretable structure. Here, we extend the notion of SPNs towards conditional distributions, which combine simple conditional models into high-dimensional ones. As shown in our experiments, the resulting conditional SPNs can be naturally used to impose structure on deep probabilistic models, allow for mixed data types, while maintaining fast and efficient inference.