Structural data well exists in Web applications, such as social networks in
social media, citation networks in academic websites, and threads data in
online forums. Due to the complex topology, it is difficult to process and make
use of the rich information within such data. Graph Neural Networks (GNNs) have
shown great advantages on learning representations for structural data.
However, the non-transparency of the deep learning models makes it non-trivial
to explain and interpret the predictions made by GNNs. Meanwhile, it is also a
big challenge to evaluate the GNN explanations, since in many cases, the
ground-truth explanations are unavailable.
In this paper, we take insights of Counterfactual and Factual (CF^2)
reasoning from causal inference theory, to solve both the learning and
evaluation problems in explainable GNNs. For generating explanations, we
propose a model-agnostic framework by formulating an optimization problem based
on both of the two casual perspectives. This distinguishes CF^2 from previous
explainable GNNs that only consider one of them. Another contribution of the
work is the evaluation of GNN explanations. For quantitatively evaluating the
generated explanations without the requirement of ground-truth, we design
metrics based on Counterfactual and Factual reasoning to evaluate the necessity
and sufficiency of the explanations. Experiments show that no matter
ground-truth explanations are available or not, CF^2 generates better
explanations than previous state-of-the-art methods on real-world datasets.
Moreover, the statistic analysis justifies the correlation between the
performance on ground-truth evaluation and our proposed metrics. Source code is
available at this https URL

本文提出了一种新的可解释 AI 方法 CF^2，结合因果推断理论的概念，通过优化问题，生成了一种两个因果视角的模型无关框架，用于产生 GNN 解释，并提供了一组基于对照和实际推理的度量方法，用于定量评估生成解释的必要性和充分性，实验证明在真实世界的数据集上，无论是否提供基本真理解释，CF^2 的生成解释都比以前的最先进方法更好。

基于反事实推理和事实推理的图神经网络解释的学习和评估

Learning and Evaluating Graph Neural Network Explanations based on  Counterfactual and Factual Reasoning

The development of a metric for structural data is a long-term problem in
pattern recognition and machine learning. In this paper, we develop a general
metric for comparing nonlinear dynamical systems that is defined with
Perron-Frobenius operators in reproducing kernel Hilbert spaces. Our metric
includes the existing fundamental metrics for dynamical systems, which are
basically defined with principal angles between some appropriately-chosen
subspaces, as its special cases. We also describe the estimation of our metric
from finite data. We empirically illustrate our metric with an example of
rotation dynamics in a unit disk in a complex plane, and evaluate the
performance with real-world time-series data.

本文通过在重现核希尔伯特空间中定义 Perron-Frobenius 算子，开发了一个用于比较非线性动力系统的通用度量，旨在解决模式识别和机器学习中长期存在的结构数据度量问题，并通过实例和真实时间序列数据进行了性能评估。