Improving Bayesian Graph Convolutional Networks using Markov Chain Monte Carlo Graph Sampling

In the modern age of social media and networks, graph representations of real-world phenomena have become incredibly crucial. Often, we are interested in understanding how entities in a graph are interconnected. Graph Neural Networks (GNNs) have proven to be a very useful tool in a variety of graph learning tasks including node classification, link prediction, and edge classification. However, in most of these tasks, the graph data we are working with may be noisy and may contain spurious edges. That is, there is a lot of uncertainty associated with the underlying graph structure. Recent approaches to modeling uncertainty have been to use a Bayesian framework and view the graph as a random variable with probabilities associated with model parameters. Introducing the Bayesian paradigm to graph-based models, specifically for semi-supervised node classification, has been shown to yield higher classification accuracies. However, the method of graph inference proposed in recent work does not take into account the structure of the graph. In this paper, we propose Neighborhood Random Walk Sampling (NRWS), a Markov Chain Monte Carlo (MCMC) based graph sampling algorithm that utilizes graph structure, improves diversity among connections, and yields consistently competitive classification results compared to the state-of-the-art in semi-supervised node classification

Deep collective inference

Collective inference is widely used to improve classification in network datasets. However, despite recent advances in deep learning and the successes of recurrent neural networks (RNNs), researchers have only just recently begun to study how to apply RNNs to heterogeneous graph and network datasets. There has been recent work on using RNNs for unsupervised learning in networks (e.g., graph clustering, node embedding) and for prediction (e.g., link prediction, graph classification), but there has been little work on using RNNs for node-based relational classification tasks. In this paper, we provide an end-to-end learning framework using RNNs for collective inference. Our main insight is to transform a node and its set of neighbors into an unordered sequence (of varying length) and use an LSTM-based RNN to predict the class label as the output of that sequence. We develop a collective inference method, which we refer to as Deep Collective Inference (DCI), that uses semi-supervised learning in partially-labeled networks and two label distribution correction mechanisms for imbalanced classes. We compare to several alternative methods on seven network datasets. DCI achieves up to a 12% reduction in error compared to the best alternative and a 25% reduction in error on average over all methods, for all label proportions

Adapting to Change: Robust Counterfactual Explanations in Dynamic Data Landscapes

We introduce a novel semi-supervised Graph Counterfactual Explainer (GCE) methodology, Dynamic GRAph Counterfactual Explainer (DyGRACE). It leverages initial knowledge about the data distribution to search for valid counterfactuals while avoiding using information from potentially outdated decision functions in subsequent time steps. Employing two graph autoencoders (GAEs), DyGRACE learns the representation of each class in a binary classification scenario. The GAEs minimise the reconstruction error between the original graph and its learned representation during training. The method involves (i) optimising a parametric density function (implemented as a logistic regression function) to identify counterfactuals by maximising the factual autoencoder's reconstruction error, (ii) minimising the counterfactual autoencoder's error, and (iii) maximising the similarity between the factual and counterfactual graphs. This semi-supervised approach is independent of an underlying black-box oracle. A logistic regression model is trained on a set of graph pairs to learn weights that aid in finding counterfactuals. At inference, for each unseen graph, the logistic regressor identifies the best counterfactual candidate using these learned weights, while the GAEs can be iteratively updated to represent the continual adaptation of the learned graph representation over iterations. DyGRACE is quite effective and can act as a drift detector, identifying distributional drift based on differences in reconstruction errors between iterations. It avoids reliance on the oracle's predictions in successive iterations, thereby increasing the efficiency of counterfactual discovery. DyGRACE, with its capacity for contrastive learning and drift detection, will offer new avenues for semi-supervised learning and explanation generation

Addressing the Impact of Localized Training Data in Graph Neural Networks

Graph Neural Networks (GNNs) have achieved notable success in learning from graph-structured data, owing to their ability to capture intricate dependencies and relationships between nodes. They excel in various applications, including semi-supervised node classification, link prediction, and graph generation. However, it is important to acknowledge that the majority of state-of-the-art GNN models are built upon the assumption of an in-distribution setting, which hinders their performance on real-world graphs with dynamic structures. In this article, we aim to assess the impact of training GNNs on localized subsets of the graph. Such restricted training data may lead to a model that performs well in the specific region it was trained on but fails to generalize and make accurate predictions for the entire graph. In the context of graph-based semi-supervised learning (SSL), resource constraints often lead to scenarios where the dataset is large, but only a portion of it can be labeled, affecting the model's performance. This limitation affects tasks like anomaly detection or spam detection when labeling processes are biased or influenced by human subjectivity. To tackle the challenges posed by localized training data, we approach the problem as an out-of-distribution (OOD) data issue by by aligning the distributions between the training data, which represents a small portion of labeled data, and the graph inference process that involves making predictions for the entire graph. We propose a regularization method to minimize distributional discrepancies between localized training data and graph inference, improving model performance on OOD data. Extensive tests on popular GNN models show significant performance improvement on three citation GNN benchmark datasets. The regularization approach effectively enhances model adaptation and generalization, overcoming challenges posed by OOD data.Comment: 6 pages, 4 figure

Bayesian Semi-supervised Learning with Graph Gaussian Processes

We propose a data-efficient Gaussian process-based Bayesian approach to the semi-supervised learning problem on graphs. The proposed model shows extremely competitive performance when compared to the state-of-the-art graph neural networks on semi-supervised learning benchmark experiments, and outperforms the neural networks in active learning experiments where labels are scarce. Furthermore, the model does not require a validation data set for early stopping to control over-fitting. Our model can be viewed as an instance of empirical distribution regression weighted locally by network connectivity. We further motivate the intuitive construction of the model with a Bayesian linear model interpretation where the node features are filtered by an operator related to the graph Laplacian. The method can be easily implemented by adapting off-the-shelf scalable variational inference algorithms for Gaussian processes.Comment: To appear in NIPS 2018 Fixed an error in Figure 2. The previous arxiv version contains two identical sub-figure