In banks, governments, and Internet companies, inconsistent data problems may often arise when various information systems are collecting, processing, and updating data due to human or equipment reasons. The emergence of inconsistent data makes it impossible to obtain correct information from the data and reduces its availability. Such problems may be fatal in data-intensive enterprises, which causes huge economic losses. Moreover, it is very difficult to clean inconsistent data in databases, especially for data containing conditional functional dependencies with built-in predicates (CFDPs), because it tends to contain more candidate repair values. For the inconsistent data containing CFD^Ps to detect incomplete and repair difficult problems in databases, we propose a dependency lifting algorithm (DLA) based on the maximum dependency set (MDS) and a reparation algorithm (C-Repair) based on integrating the minimum cost and attribute correlation, respectively. In detection, we find recessive dependencies from the original dependency set to obtain the MDS and improve the original algorithm by dynamic domain adjustment, which extends the applicability to continuous attributes and improves the detection accuracy. In reparation, we first set up a priority queue (PQ) for elements to be repaired based on the minimum cost idea to select a candidate element; then, we treat the corresponding conflict-free instance ( $I_{nv}$ ) as the training set to learn the correlation among attributes and compute the weighted distance (WDis) between the tuple of the candidate element and other tuples in $I_{nv}$ according to the correlation; and, lastly, we perform reparation based on the WDis and re-compute the PQ after each reparation round to improve the efficiency, and use a label, flag, to mark the repaired elements to ensure the convergence at the same time. By setting up a contrast experiment, we compare the DLA with the CFD^Ps based algorithm, and the C-Repair with a cost-based, interpolation-based algorithm on a simulated instance and a real instance. From the experimental results, the DLA and C-Repair algorithms have better detection and repair ability at a higher time cost.

Federated Learning (FL) is a promising distributed machine learning framework that emphasizes privacy protection. However, inconsistencies between local optimization objectives and the global objective, commonly referred to as client drift, primarily arise due to non-independently and identically distributed (Non-IID) data, multiple local training steps, and partial client participation in training. The majority of current research tackling this challenge is mainly based on the empirical risk minimization (ERM) principle, while giving little consideration to the connection between the global loss landscape and generalization capability. This study proposes FedGAM, an innovative FL algorithm that incorporates Gradient Norm-Aware Minimization (GAM) to efficiently search for a local flat landscape. FedGAM specifically modifies the client model training objective to simultaneously minimize the loss value and first-order flatness, thereby seeking flat minima. To directly smooth the global flatness, we propose the more significant FedGAM-CV, which employs control variables to correct local updates, guiding each client to train models in a globally flat direction. Experiments on three datasets (CIFAR-10, MNIST, and FashionMNIST) demonstrate that our proposed algorithms outperform existing FL baselines, effectively finding flat minima and addressing the client drift problem.

In banks, governments, and internet companies, due to the increasing demand for data in various information systems and continuously shortening of the cycle for data collection and update, there may be a variety of data quality issues in a database. As the expansion of data scales, methods such as pre-specifying business rules or introducing expert experience into a repair process are no longer applicable to some information systems requiring rapid responses. In this case, we divided data cleaning into supervised and unsupervised forms according to whether there were interventions in the repair processes and put forward a new dimension suitable for unsupervised cleaning in this paper. For weak logic errors in unsupervised data cleaning, we proposed an attribute correlation-based (ACB)-Framework under blocking, and designed three different data blocking methods to reduce the time complexity and test the impact of clustering accuracy on data cleaning. The experiments showed that the blocking methods could effectively reduce the repair time by maintaining the repair validity. Moreover, we concluded that the blocking methods with a too high clustering accuracy tended to put tuples with the same elements into a data block, which reduced the cleaning ability. In summary, the ACB-Framework with blocking can reduce the corresponding time cost and does not need the guidance of domain knowledge or interventions in repair, which can be applied in information systems requiring rapid responses, such as internet web pages, network servers, and sensor information acquisition.