Optimal Cost-Effective Maintenance Policy for a Helicopter Gearbox Early Fault Detection under Varying Load

Most of the existing fault detection methods rarely consider the cost-optimal maintenance policy. A novel multivariate Bayesian control approach is proposed, which enables the implementation of early fault detection for a helicopter gearbox with cost minimization maintenance policy under varying load. A continuous time hidden semi-Markov model (HSMM) is employed to describe the stochastic relationship between the unobservable states and observable observations of the gear system. Explicit expressions for the remaining useful life prediction are derived using HSMM. Considering the maintenance cost in fault detection, the multivariate Bayesian control scheme based on HSMM is developed; the objective is to minimize the long-run expected average cost per unit time. An effective computational algorithm in the semi-Markov decision process (SMDP) framework is designed to obtain the optimal control limit. A comparison with the multivariate Bayesian control chart based on hidden Markov model (HMM) and the traditional age-based replacement policy is given, which illustrates the effectiveness of the proposed approach

Dual Node and Edge Fairness-Aware Graph Partition

Fair graph partition of social networks is a crucial step toward ensuring fair and non-discriminatory treatments in unsupervised user analysis. Current fair partition methods typically consider node balance, a notion pursuing a proportionally balanced number of nodes from all demographic groups, but ignore the bias induced by imbalanced edges in each cluster. To address this gap, we propose a notion edge balance to measure the proportion of edges connecting different demographic groups in clusters. We analyze the relations between node balance and edge balance, then with line graph transformations, we propose a co-embedding framework to learn dual node and edge fairness-aware representations for graph partition. We validate our framework through several social network datasets and observe balanced partition in terms of both nodes and edges along with good utility. Moreover, we demonstrate our fair partition can be used as pseudo labels to facilitate graph neural networks to behave fairly in node classification and link prediction tasks

Mining Label Distribution Drift in Unsupervised Domain Adaptation

Unsupervised domain adaptation targets to transfer task knowledge from labeled source domain to related yet unlabeled target domain, and is catching extensive interests from academic and industrial areas. Although tremendous efforts along this direction have been made to minimize the domain divergence, unfortunately, most of existing methods only manage part of the picture by aligning feature representations from different domains. Beyond the discrepancy in feature space, the gap between known source label and unknown target label distribution, recognized as label distribution drift, is another crucial factor raising domain divergence, and has not been paid enough attention and well explored. From this point, in this paper, we first experimentally reveal how label distribution drift brings negative effects on current domain adaptation methods. Next, we propose Label distribution Matching Domain Adversarial Network (LMDAN) to handle data distribution shift and label distribution drift jointly. In LMDAN, label distribution drift problem is addressed by the proposed source samples weighting strategy, which select samples to contribute to positive adaptation and avoid negative effects brought by the mismatched in label distribution. Finally, different from general domain adaptation experiments, we modify domain adaptation datasets to create the considerable label distribution drift between source and target domain. Numerical results and empirical model analysis show that LMDAN delivers superior performance compared to other state-of-the-art domain adaptation methods under such scenarios

The Numerical Invariant Measure of Stochastic Differential Equations With Markovian Switching

The existence and uniqueness of the numerical invariant measure of the backward Euler-Maruyama method for stochastic differential equations with Markovian switching is yielded, and it is revealed that the numerical invariant measure converges to the underlying invariant measure in the Wasserstein metric. Under the polynomial growth condition of drift term the convergence rate is estimated. The global Lipschitz condition on the drift coefficients required by Bao et al., 2016 and Yuan et al., 2005 is released. Several examples and numerical experiments are given to verify our theory.Comment: 25 pages, 4 figure

Characterizing the Influence of Graph Elements

Influence function, a method from robust statistics, measures the changes of model parameters or some functions about model parameters concerning the removal or modification of training instances. It is an efficient and useful post-hoc method for studying the interpretability of machine learning models without the need for expensive model re-training. Recently, graph convolution networks (GCNs), which operate on graph data, have attracted a great deal of attention. However, there is no preceding research on the influence functions of GCNs to shed light on the effects of removing training nodes/edges from an input graph. Since the nodes/edges in a graph are interdependent in GCNs, it is challenging to derive influence functions for GCNs. To fill this gap, we started with the simple graph convolution (SGC) model that operates on an attributed graph and formulated an influence function to approximate the changes in model parameters when a node or an edge is removed from an attributed graph. Moreover, we theoretically analyzed the error bound of the estimated influence of removing an edge. We experimentally validated the accuracy and effectiveness of our influence estimation function. In addition, we showed that the influence function of an SGC model could be used to estimate the impact of removing training nodes/edges on the test performance of the SGC without re-training the model. Finally, we demonstrated how to use influence functions to guide the adversarial attacks on GCNs effectively