The ability to detect when a system undergoes an incipient fault is of
paramount importance in preventing a critical failure. In this work, we propose
an information-driven fault detection method based on a novel concept drift
detector. The method is tailored to identifying drifts in input-output
relationships of additive noise models (i.e., model drifts) and is based on a
distribution-free mutual information (MI) estimator. Our scheme does not
require prior faulty examples and can be applied distribution-free over a large
class of system models. Our core contributions are twofold. First, we
demonstrate the connection between fault detection, model drift detection, and
testing independence between two random variables. Second, we prove several
theoretical properties of the proposed MI-based fault detection scheme: (i)
strong consistency, (ii) exponentially fast detection of the non-faulty case,
and (iii) control of both significance levels and power of the test. To
conclude, we validate our theory with synthetic data and the benchmark dataset
N-CMAPSS of aircraft turbofan engines. These empirical results support the
usefulness of our methodology in many practical and realistic settings, and the
theoretical results show performance guarantees that other methods cannot
offer.

基于新颖的概念漂移检测器，我们提出了一种以信息驱动的故障检测方法，适用于识别加性噪声模型的输入输出关系中的漂移（即模型漂移），该方案不需要事先的故障示例，并且可以在系统模型的大类上无分布地应用。通过与故障检测、模型漂移检测以及两个随机变量之间的相互独立性测试之间的关联，我们证明了所提出的基于互信息的故障检测方案具有强一致性、对非故障情况的指数快速检测以及对检验的显著性水平和功率的控制等几个理论特性。通过合成数据和飞机涡轮发动机的基准数据集 N-CMAPSS 的验证，我们的理论得到了支持，结果表明我们的方法在许多实际和现实的场景中具有实用性，并且其他方法无法提供的理论结果显示了性能保证。

基于信息驱动策略的故障检测和监控：方法、理论和应用

Fault Detection and Monitoring using an Information-Driven Strategy:  Method, Theory, and Application

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.

通过引入信息瓶颈理论的设计，结合相似桥接原理和互信息估计式的互动，提出了一种新型的子图信息瓶颈架构来识别预测压缩的子图，成功去除了图数据中的噪音和冗余，具有高效和稳定性，得到了较好的优化结果和理论边界。

利用子图信息识别具有预测性的基础结构压缩模型

Recognizing Predictive Substructures with Subgraph 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。