Hansheng Wang

Shuyuan Wu, Danyang Huang, Hansheng Wang

We study a fully decentralized federated learning algorithm, which is a novel gradient descent algorithm executed on a communication-based network. For convenience, we refer to it as a network gradient descent (NGD) method. In the NGD method, only statistics (e.g., parameter estimates) need to be communicated, minimizing the risk of privacy. Meanwhile, different clients communicate with each other directly according to a carefully designed network structure without a central master. This greatly enhances the reliability of the entire algorithm. Those nice properties inspire us to carefully study the NGD method both theoretically and numerically. Theoretically, we start with a classical linear regression model. We find that both the learning rate and the network structure play significant roles in determining the NGD estimator's statistical efficiency. The resulting NGD estimator can be statistically as efficient as the global estimator, if the learning rate is sufficiently small and the network structure is well balanced, even if the data are distributed heterogeneously. Those interesting findings are then extended to general models and loss functions. Extensive numerical studies are presented to corroborate our theoretical findings. Classical deep learning models are also presented for illustration purpose.

Qianhan Zeng, Yingqiu Zhu, Xuening Zhu et al.

Labeling mistakes are frequently encountered in real-world applications. If not treated well, the labeling mistakes can deteriorate the classification performances of a model seriously. To address this issue, we propose an improved Naive Bayes method for text classification. It is analytically simple and free of subjective judgements on the correct and incorrect labels. By specifying the generating mechanism of incorrect labels, we optimize the corresponding log-likelihood function iteratively by using an EM algorithm. Our simulation and experiment results show that the improved Naive Bayes method greatly improves the performances of the Naive Bayes method with mislabeled data.

Jing Zhou, Xinru Jing, Muyu Liu et al.

In this paper, we propose a dictionary screening method for embedding compression in text classification tasks. The key purpose of this method is to evaluate the importance of each keyword in the dictionary. To this end, we first train a pre-specified recurrent neural network-based model using a full dictionary. This leads to a benchmark model, which we then use to obtain the predicted class probabilities for each sample in a dataset. Next, to evaluate the impact of each keyword in affecting the predicted class probabilities, we develop a novel method for assessing the importance of each keyword in a dictionary. Consequently, each keyword can be screened, and only the most important keywords are reserved. With these screened keywords, a new dictionary with a considerably reduced size can be constructed. Accordingly, the original text sequence can be substantially compressed. The proposed method leads to significant reductions in terms of parameters, average text sequence, and dictionary size. Meanwhile, the prediction power remains very competitive compared to the benchmark model. Extensive numerical studies are presented to demonstrate the empirical performance of the proposed method.

Shuyuan Wu, Feifei Wang, Yuan Gao et al.

In decentralized federated learning (DFL), the presence of abnormal clients, often caused by noisy or poisoned data, can significantly disrupt the learning process and degrade the overall robustness of the model. Previous methods on this issue often require a sufficiently large number of normal neighboring clients or prior knowledge of reliable clients, which reduces the practical applicability of DFL. To address these limitations, we develop here a novel adaptive DFL (aDFL) approach for robust estimation. The key idea is to adaptively adjust the learning rates of clients. By assigning smaller rates to suspicious clients and larger rates to normal clients, aDFL mitigates the negative impact of abnormal clients on the global model in a fully adaptive way. Our theory does not put any stringent conditions on neighboring nodes and requires no prior knowledge. A rigorous convergence analysis is provided to guarantee the oracle property of aDFL. Extensive numerical experiments demonstrate the superior performance of the aDFL method.

Xuetong Li, Yuan Gao, Hong Chang et al.

This paper presents a selective review of statistical computation methods for massive data analysis. A huge amount of statistical methods for massive data computation have been rapidly developed in the past decades. In this work, we focus on three categories of statistical computation methods: (1) distributed computing, (2) subsampling methods, and (3) minibatch gradient techniques. The first class of literature is about distributed computing and focuses on the situation, where the dataset size is too huge to be comfortably handled by one single computer. In this case, a distributed computation system with multiple computers has to be utilized. The second class of literature is about subsampling methods and concerns about the situation, where the sample size of dataset is small enough to be placed on one single computer but too large to be easily processed by its memory as a whole. The last class of literature studies those minibatch gradient related optimization techniques, which have been extensively used for optimizing various deep learning models.

Yuling Jiao, Wensen Ma, Defeng Sun et al.

In this paper, we propose a novel self-supervised transfer learning method called \underline{\textbf{D}}istribution \underline{\textbf{M}}atching (DM), which drives the representation distribution toward a predefined reference distribution while preserving augmentation invariance. DM results in a learned representation space that is intuitively structured and therefore easy to interpret. Experimental results across multiple real-world datasets and evaluation metrics demonstrate that DM performs competitively on target classification tasks compared to existing self-supervised transfer learning methods. Additionally, we provide robust theoretical guarantees for DM, including a population theorem and an end-to-end sample theorem. The population theorem bridges the gap between the self-supervised learning task and target classification accuracy, while the sample theorem shows that, even with a limited number of samples from the target domain, DM can deliver exceptional classification performance, provided the unlabeled sample size is sufficiently large.

H. Wang, Y. Pang, D. Shang

In this study, the novel hybrid machine learning approach is proposed in carbon price fluctuation prediction. Specifically, a research framework integrating DILATED Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) neural network algorithm is proposed. The advantage of the combined framework is that it can make feature extraction more efficient. Then, based on the DILATED CNN-LSTM framework, the L1 and L2 parameter norm penalty as regularization method is adopted to predict. Referring to the characteristics of high correlation between energy indicator price and blockchain information in previous literature, and we primarily includes indicators related to blockchain information through regularization process. Based on the above methods, this paper uses a dataset containing an amount of data to carry out the carbon price prediction. The experimental results show that the DILATED CNN-LSTM framework is superior to the traditional CNN-LSTM architecture. Blockchain information can effectively predict the price. Since parameter norm penalty as regularization, Ridge Regression (RR) as L2 regularization is better than Smoothly Clipped Absolute Deviation Penalty (SCAD) as L1 regularization in price forecasting. Thus, the proposed RR-DILATED CNN-LSTM approach can effectively and accurately predict the fluctuation trend of the carbon price. Therefore, the new forecasting methods and theoretical ecology proposed in this study provide a new basis for trend prediction and evaluating digital assets policy represented by the carbon price for both the academia and practitioners.

Tao Zou, Xian Li, Xuan Liang et al.

This article introduces subbagging (subsample aggregating) estimation approaches for big data analysis with memory constraints of computers. Specifically, for the whole dataset with size $N$, $m_N$ subsamples are randomly drawn, and each subsample with a subsample size $k_N\ll N$ to meet the memory constraint is sampled uniformly without replacement. Aggregating the estimators of $m_N$ subsamples can lead to subbagging estimation. To analyze the theoretical properties of the subbagging estimator, we adapt the incomplete $U$-statistics theory with an infinite order kernel to allow overlapping drawn subsamples in the sampling procedure. Utilizing this novel theoretical framework, we demonstrate that via a proper hyperparameter selection of $k_N$ and $m_N$, the subbagging estimator can achieve $\sqrt{N}$-consistency and asymptotic normality under the condition $(k_Nm_N)/N\to α\in (0,\infty]$. Compared to the full sample estimator, we theoretically show that the $\sqrt{N}$-consistent subbagging estimator has an inflation rate of $1/α$ in its asymptotic variance. Simulation experiments are presented to demonstrate the finite sample performances. An American airline dataset is analyzed to illustrate that the subbagging estimate is numerically close to the full sample estimate, and can be computationally fast under the memory constraint.

Yingying Ma, Hansheng Wang

Massive data analysis becomes increasingly prevalent, subsampling methods like BLB (Bag of Little Bootstraps) serves as powerful tools for assessing the quality of estimators for massive data. However, the performance of the subsampling methods are highly influenced by the selection of tuning parameters ( e.g., the subset size, number of resamples per subset ). In this article we develop a hyperparameter selection methodology, which can be used to select tuning parameters for subsampling methods. Specifically, by a careful theoretical analysis, we find an analytically simple and elegant relationship between the asymptotic efficiency of various subsampling estimators and their hyperparameters. This leads to an optimal choice of the hyperparameters. More specifically, for an arbitrarily specified hyperparameter set, we can improve it to be a new set of hyperparameters with no extra CPU time cost, but the resulting estimator's statistical efficiency can be much improved. Both simulation studies and real data analysis demonstrate the superior advantage of our method.

Yingqiu Zhu, Yu Chen, Danyang Huang et al.

In deep learning tasks, the learning rate determines the update step size in each iteration, which plays a critical role in gradient-based optimization. However, the determination of the appropriate learning rate in practice typically replies on subjective judgement. In this work, we propose a novel optimization method based on local quadratic approximation (LQA). In each update step, given the gradient direction, we locally approximate the loss function by a standard quadratic function of the learning rate. Then, we propose an approximation step to obtain a nearly optimal learning rate in a computationally efficient way. The proposed LQA method has three important features. First, the learning rate is automatically determined in each update step. Second, it is dynamically adjusted according to the current loss function value and the parameter estimates. Third, with the gradient direction fixed, the proposed method leads to nearly the greatest reduction in terms of the loss function. Extensive experiments have been conducted to prove the strengths of the proposed LQA method.