Graph Neural Networks (GNNs) have received increasing attention due to their
ability to learn from graph-structured data. To open the black-box of these
deep learning models, post-hoc instance-level explanation methods have been
proposed to understand GNN predictions. These methods seek to discover
substructures that explain the prediction behavior of a trained GNN. In this
paper, we show analytically that for a large class of explanation tasks,
conventional approaches, which are based on the principle of graph information
bottleneck (GIB), admit trivial solutions that do not align with the notion of
explainability. Instead, we argue that a modified GIB principle may be used to
avoid the aforementioned trivial solutions. We further introduce a novel
factorized explanation model with theoretical performance guarantees. The
modified GIB is used to analyze the structural properties of the proposed
factorized explainer. We conduct extensive experiments on both synthetic and
real-world datasets to validate the effectiveness of our proposed factorized
explainer over existing approaches.

我们展示了在传统方法无法获得满足可解释性准则的解释时，一种基于修改后的图信息瓶颈原理的因子解释模型的有效性，并进行了广泛实验证实。

图神经网络的因子化解释器

Factorized Explainer for Graph Neural Networks

Graph Neural Networks (GNNs) have received increasing attention due to their
ability to learn from graph-structured data. However, their predictions are
often not interpretable. Post-hoc instance-level explanation methods have been
proposed to understand GNN predictions. These methods seek to discover
substructures that explain the prediction behavior of a trained GNN. In this
paper, we shed light on the existence of the distribution shifting issue in
existing methods, which affects explanation quality, particularly in
applications on real-life datasets with tight decision boundaries. To address
this issue, we introduce a generalized Graph Information Bottleneck (GIB) form
that includes a label-independent graph variable, which is equivalent to the
vanilla GIB. Driven by the generalized GIB, we propose a graph mixup method,
MixupExplainer, with a theoretical guarantee to resolve the distribution
shifting issue. We conduct extensive experiments on both synthetic and
real-world datasets to validate the effectiveness of our proposed mixup
approach over existing approaches. We also provide a detailed analysis of how
our proposed approach alleviates the distribution shifting issue.

针对图神经网络（GNN）通常难以解释的问题，本文提出了一种基于 Graph Information Bottleneck 的 MixupExplainer 方法，通过加入一个与标签无关的图变量来解决现有的方法存在的分布转移问题，并通过实验验证了该方法的有效性。

MixupExplainer：利用数据增强泛化图神经网络解释

MixupExplainer: Generalizing Explanations for Graph Neural Networks with  Data Augmentation

Subgraph recognition aims at discovering a compressed substructure of a graph
that is most informative to the graph property. It can be formulated by
optimizing Graph Information Bottleneck (GIB) with a mutual information
estimator. However, GIB suffers from training instability and degenerated
results due to its intrinsic optimization process. To tackle these issues, we
reformulate the subgraph recognition problem into two steps: graph perturbation
and subgraph selection, leading to a novel Variational Graph Information
Bottleneck (VGIB) framework. VGIB first employs the noise injection to modulate
the information flow from the input graph to the perturbed graph. Then, the
perturbed graph is encouraged to be informative to the graph property. VGIB
further obtains the desired subgraph by filtering out the noise in the
perturbed graph. With the customized noise prior for each input, the VGIB
objective is endowed with a tractable variational upper bound, leading to a
superior empirical performance as well as theoretical properties. Extensive
experiments on graph interpretation, explainability of Graph Neural Networks,
and graph classification show that VGIB finds better subgraphs than existing
methods. Code is avaliable at this https URL

该研究提出了一种名为 Variational Graph Information Bottleneck (VGIB) 的框架，用于识别图形中最具信息量的压缩子结构，VGIB 通过对图形施加噪声注入的方式，再通过过滤噪声来获得所需的子图，并在图解释、图神经网络的可解释性和图分类等方面进行了广泛实验。

利用变分图信息瓶颈改进子图识别

Improving Subgraph Recognition with Variational Graph Information  Bottleneck

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.

本文提出了图信息瓶颈（GIB）框架，解决了深度图学习中子图识别问题，并在三种应用场景下评估 IB 子图的性能。