Wei Zhu

Jiaju Miao, Wei Zhu

The classification of imbalanced data has presented a significant challenge for most well-known classification algorithms that were often designed for data with relatively balanced class distributions. Nevertheless skewed class distribution is a common feature in real world problems. It is especially prevalent in certain application domains with great need for machine learning and better predictive analysis such as disease diagnosis, fraud detection, bankruptcy prediction, and suspect identification. In this paper, we propose a novel tree-based algorithm based on the area under the precision-recall curve (AUPRC) for variable selection in the classification context. Our algorithm, named as the "Precision-Recall Curve classification tree", or simply the "PRC classification tree" modifies two crucial stages in tree building. The first stage is to maximize the area under the precision-recall curve in node variable selection. The second stage is to maximize the harmonic mean of recall and precision (F-measure) for threshold selection. We found the proposed PRC classification tree, and its subsequent extension, the PRC random forest, work well especially for class-imbalanced data sets. We have demonstrated that our methods outperform their classic counterparts, the usual CART and random forest for both synthetic and real data. Furthermore, the ROC classification tree proposed by our group previously has shown good performance in imbalanced data. The combination of them, the PRC-ROC tree, also shows great promise in identifying the minority class.

Pengzhan Guo, Zeyang Ye, Keli Xiao et al.

This paper investigates the stochastic optimization problem with a focus on developing scalable parallel algorithms for deep learning tasks. Our solution involves a reformation of the objective function for stochastic optimization in neural network models, along with a novel parallel strategy, coined weighted aggregating stochastic gradient descent (WASGD). Following a theoretical analysis on the characteristics of the new objective function, WASGD introduces a decentralized weighted aggregating scheme based on the performance of local workers. Without any center variable, the new method automatically assesses the importance of local workers and accepts them according to their contributions. Furthermore, we have developed an enhanced version of the method, WASGD+, by (1) considering a designed sample order and (2) applying a more advanced weight evaluating function. To validate the new method, we benchmark our schemes against several popular algorithms including the state-of-the-art techniques (e.g., elastic averaging SGD) in training deep neural networks for classification tasks. Comprehensive experiments have been conducted on four classic datasets, including the CIFAR-100, CIFAR-10, Fashion-MNIST, and MNIST. The subsequent results suggest the superiority of the WASGD scheme in accelerating the training of deep architecture. Better still, the enhanced version, WASGD+, has been shown to be a significant improvement over its basic version.

Min Shu, Wei Zhu

The application of rough set theory in incomplete information systems is a key problem in practice since missing values almost always occur in knowledge acquisition due to the error of data measuring, the limitation of data collection, or the limitation of data comprehension, etc. An incomplete information system is mainly processed by compressing the indiscernibility relation. The existing rough set extension models based on tolerance or symmetric similarity relations typically discard one relation among the reflexive, symmetric and transitive relations, especially the transitive relation. In order to overcome the limitations of the current rough set extension models, we define a new relation called the positive transitive relation and then propose a novel rough set extension model built upon which. The new model holds the merit of the existing rough set extension models while avoids their limitations of discarding transitivity or symmetry. In comparison to the existing extension models, the proposed model has a better performance in processing the incomplete information systems while substantially reducing the computational complexity, taking into account the relation of tolerance and similarity of positive transitivity, and supplementing the related theories in accordance to the intuitive classification of incomplete information. In summary, the positive transitive relation can improve current theoretical analysis of incomplete information systems and the newly proposed extension model is more suitable for processing incomplete information systems and has a broad application prospect.

Hao Han, Wei Zhu

The errors-in-variables (EIV) regression model, being more realistic by accounting for measurement errors in both the dependent and the independent variables, is widely adopted in applied sciences. The traditional EIV model estimators, however, can be highly biased by outliers and other departures from the underlying assumptions. In this paper, we develop a novel nonparametric regression approach - the robust compound regression (RCR) analysis method for the robust estimation of EIV models. We first introduce a robust and efficient estimator called least sine squares (LSS). Taking full advantage of both the new LSS method and the compound regression analysis method developed in our own group, we subsequently propose the RCR approach as a generalization of those two, which provides a robust counterpart of the entire class of the maximum likelihood estimation (MLE) solutions of the EIV model, in a 1-1 mapping. Technically, our approach gives users the flexibility to select from a class of RCR estimates the optimal one with a predefined regression efficiency criterion satisfied. Simulation studies and real-life examples are provided to illustrate the effectiveness of the RCR approach.