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Register a new userRecognizing Predictive Substructures with Subgraph Information Bottleneck
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Junchi Yu
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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The emergence of Graph Convolutional Network (GCN) has greatly boosted the progress of graph learning. However, two disturbing factors, noise and redundancy in graph data, and lack of interpretation for prediction results, impede further development of GCN. One solution is to recognize a predictive yet compressed subgraph to get rid of the noise and redundancy and obtain the interpretable part of the graph. This setting of subgraph is similar to the information bottleneck (IB) principle, which is less studied on graph-structured data and GCN. Inspired by the IB principle, we propose a novel subgraph information bottleneck (SIB) framework to recognize such subgraphs, named IB-subgraph. However, the intractability of mutual information and the discrete nature of graph data makes the objective of SIB notoriously hard to optimize. To this end, we introduce a bilevel optimization scheme coupled with a mutual information estimator for irregular graphs. Moreover, we propose a continuous relaxation for subgraph selection with a connectivity loss for stabilization. We further theoretically prove the error bound of our estimation scheme for mutual information and the noise-invariant nature of IB-subgraph. Extensive experiments on graph learning and large-scale point cloud tasks demonstrate the superior property of IB-subgraph.
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Given the input graph and its label/property, several key problems of graph learning, such as finding interpretable subgraphs, graph denoising and graph compression, can be attributed to the fundamental problem of recognizing a subgraph of the original one. This subgraph shall be as informative as possible, yet contains less redundant and noisy structure. This problem setting is closely related to the well-known information bottleneck (IB) principle, which, however, has less been studied for the irregular graph data and graph neural networks (GNNs). In this paper, we propose a framework of Graph Information Bottleneck (GIB) for the subgraph recognition problem in deep graph learning. Under this framework, one can recognize the maximally informative yet compressive subgraph, named IB-subgraph. However, the GIB objective is notoriously hard to optimize, mostly due to the intractability of the mutual information of irregular graph data and the unstable optimization process. In order to tackle these challenges, we propose: i) a GIB objective based-on a mutual information estimator for the irregular graph data; ii) a bi-level optimization scheme to maximize the GIB objective; iii) a connectivity loss to stabilize the optimization process. We evaluate the properties of the IB-subgraph in three application scenarios: improvement of graph classification, graph interpretation and graph denoising. Extensive experiments demonstrate that the information-theoretic IB-subgraph enjoys superior graph properties.
Graph representation learning has attracted increasing research attention. However, most existing studies fuse all structural features and node attributes to provide an overarching view of graphs, neglecting finer substructures semantics, and suffering from interpretation enigmas. This paper presents a novel hierarchical subgraph-level selection and embedding based graph neural network for graph classification, namely SUGAR, to learn more discriminative subgraph representations and respond in an explanatory way. SUGAR reconstructs a sketched graph by extracting striking subgraphs as the representative part of the original graph to reveal subgraph-level patterns. To adaptively select striking subgraphs without prior knowledge, we develop a reinforcement pooling mechanism, which improves the generalization ability of the model. To differentiate subgraph representations among graphs, we present a self-supervised mutual information mechanism to encourage subgraph embedding to be mindful of the global graph structural properties by maximizing their mutual information. Extensive experiments on six typical bioinformatics datasets demonstrate a significant and consistent improvement in model quality with competitive performance and interpretability.
The information bottleneck (IB) method is a technique for extracting information that is relevant for predicting the target random variable from the source random variable, which is typically implemented by optimizing the IB Lagrangian that balances the compression and prediction terms. However, the IB Lagrangian is hard to optimize, and multiple trials for tuning values of Lagrangian multiplier are required. Moreover, we show that the prediction performance strictly decreases as the compression gets stronger during optimizing the IB Lagrangian. In this paper, we implement the IB method from the perspective of supervised disentangling. Specifically, we introduce Disentangled Information Bottleneck (DisenIB) that is consistent on compressing source maximally without target prediction performance loss (maximum compression). Theoretical and experimental results demonstrate that our method is consistent on maximum compression, and performs well in terms of generalization, robustness to adversarial attack, out-of-distribution detection, and supervised disentangling.
Initialization plays a critical role in the training of deep neural networks (DNN). Existing initialization strategies mainly focus on stabilizing the training process to mitigate gradient vanish/explosion problems. However, these initialization methods are lacking in consideration about how to enhance generalization ability. The Information Bottleneck (IB) theory is a well-known understanding framework to provide an explanation about the generalization of DNN. Guided by the insights provided by IB theory, we design two criteria for better initializing DNN. And we further design a neuron campaign initialization algorithm to efficiently select a good initialization for a neural network on a given dataset. The experiments on MNIST dataset show that our method can lead to a better generalization performance with faster convergence.
We propose a new approach to train a variational information bottleneck (VIB) that improves its robustness to adversarial perturbations. Unlike the traditional methods where the hard labels are usually used for the classification task, we refine the categorical class information in the training phase with soft labels which are obtained from a pre-trained reference neural network and can reflect the likelihood of the original class labels. We also relax the Gaussian posterior assumption in the VIB implementation by using the mutual information neural estimation. Extensive experiments have been performed with the MNIST and CIFAR-10 datasets, and the results show that our proposed approach significantly outperforms the benchmarked models.
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