Gaussian process regression (GPR) is an important nonparametric learning method in machine learning research with many real-world applications. It is well known that training large-scale GPR is a challenging task due to the required heavy computational cost and large volume memory. To address this challenging problem, in this article, we propose an asynchronous doubly stochastic gradient algorithm to handle the large-scale training of GPR. We formulate the GPR to a convex optimization problem, i.e., kernel ridge regression. After that, in order to efficiently solve this convex kernel problem, we first use the random feature mapping method to approximate the kernel model and then utilize two unbiased stochastic approximations, i.e., stochastic variance reduced gradient and stochastic coordinate descent, to update the solution asynchronously and in parallel. In this way, our algorithm scales well in both sample size and dimensionality, and speeds up the training computation. More importantly, we prove that our algorithm has a global linear convergence rate. Our experimental results on eight large-scale benchmark datasets with both regression and classification tasks show that the proposed algorithm outperforms the existing state-of-the-art GPR methods.

The clustering methods have absorbed even-increasing attention in machine learning and computer vision communities in recent years. In this article, we focus on the real-world applications where a sample can be represented by multiple views. Traditional methods learn a common latent space for multiview samples without considering the diversity of multiview representations and use K -means to obtain the final results, which are time and space consuming. On the contrary, we propose a novel end-to-end deep multiview clustering model with collaborative learning to predict the clustering results directly. Specifically, multiple autoencoder networks are utilized to embed multi-view data into various latent spaces and a heterogeneous graph learning module is employed to fuse the latent representations adaptively, which can learn specific weights for different views of each sample. In addition, intraview collaborative learning is framed to optimize each single-view clustering task and provide more discriminative latent representations. Simultaneously, interview collaborative learning is employed to obtain complementary information and promote consistent cluster structure for a better clustering solution. Experimental results on several datasets show that our method significantly outperforms several state-of-the-art clustering approaches.

Learning to improve AUC performance for imbalanced data is an important machine learning research problem. Most methods of AUC maximization assume that the model function is linear in the original feature space. However, this assumption is not suitable for nonlinear separable problems. Although there have been some nonlinear methods of AUC maximization, scaling up nonlinear AUC maximization is still an open question. To address this challenging problem, in this paper, we propose a novel large-scale nonlinear AUC maximization method (named as TSAM) based on the triply stochastic gradient descents. Specifically, we first use the random Fourier feature to approximate the kernel function. After that, we use the triply stochastic gradients w.r.t. the pairwise loss and random feature to iteratively update the solution. Finally, we prove that TSAM converges to the optimal solution with the rate of O(1/t) after t iterations. Experimental results on a variety of benchmark datasets not only confirm the scalability of TSAM, but also show a significant reduction of computational time compared with existing batch learning algorithms, while retaining the similar generalization performance.

Kernel methods have achieved tremendous success in the past two decades. In the current big data era, data collection has grown tremendously. However, existing kernel methods are not scalable enough both at the training and predicting steps. To address this challenge, in this paper, we first introduce a general sparse kernel learning formulation based on the random feature approximation, where the loss functions are possibly non-convex. In order to reduce the scale of random features required in experiment, we also use that formulation based on the orthogonal random feature approximation. Then we propose a new asynchronous parallel doubly stochastic algorithm for large scale sparse kernel learning (AsyDSSKL). To the best our knowledge, AsyDSSKL is the first algorithm with the techniques of asynchronous parallel computation and doubly stochastic optimization. We also provide a comprehensive convergence guarantee to AsyDSSKL. Importantly, the experimental results on various large-scale real-world datasets show that, our AsyDSSKL method has the significant superiority on the computational efficiency at the training and predicting steps over the existing kernel methods.

Vertical federated learning (VFL) attracts increasing attention due to the emerging demands of multi-party collaborative modeling and concerns of privacy leakage. A complete list of metrics to evaluate VFL algorithms should include model applicability, privacy security, communication cost, and computation efficiency, where privacy security is especially important to VFL. However, to the best of our knowledge, there does not exist a VFL algorithm satisfying all these criteria very well. To address this challenging problem, in this paper, we reveal that zeroth-order optimization (ZOO) is a desirable companion for VFL. Specifically, ZOO can 1) improve the model applicability of VFL framework, 2) prevent VFL framework from privacy leakage under curious, colluding, and malicious threat models, 3) support inexpensive communication and efficient computation. Based on that, we propose a novel and practical VFL framework with black-box models, which is inseparably interconnected to the promising properties of ZOO. We believe that it takes one stride towards designing a practical VFL framework matching all the criteria. Under this framework, we raise two novel asynchronous zeroth-order algorithms for vertical federated learning (AsyREVEL) with different smoothing techniques. We theoretically drive the convergence rates of AsyREVEL algorithms under nonconvex condition. More importantly, we prove the privacy security of our proposed framework under existing VFL attacks on different levels. Extensive experiments on benchmark datasets demonstrate the favorable model applicability, satisfied privacy security, inexpensive communication, efficient computation, scalability and losslessness of our framework.

Graph convolution networks (GCNs) are a powerful deep learning approach and have been successfully applied to representation learning on graphs in a variety of real-world applications. Despite their success, two fundamental weaknesses of GCNs limit their ability to represent graph-structured data: poor performance when labeled data are severely scarce and indistinguishable features when more layers are stacked. In this paper, we propose a simple yet effective Self-Supervised Semantic Alignment Graph Convolution Network (SelfSAGCN), which consists of two crux techniques: Identity Aggregation and Semantic Alignment, to overcome these weaknesses. The behind basic idea is the node features in the same class but learned from semantic and graph structural aspects respectively, are expected to be mapped nearby. Specifically, the Identity Aggregation is applied to extract semantic features from labeled nodes, the Semantic Alignment is utilized to align node features obtained from different aspects using the class central similarity. In this way, the over-smoothing phenomenon is alleviated, while the similarities between the unlabeled features and labeled ones from the same class are enhanced. Experimental results on five popular datasets show that the proposed SelfSAGCN outperforms state-of-the-art methods on various classification tasks.

Deep clustering gradually becomes an important branch in unsupervised learning methods. However, current approaches hardly take into consideration the semantic sample relationships that existed in both local and global features. In addition, since the deep features are updated on-the-fly, relying on these sample relationships may construct more semantically confident sample pairs, leading to inferior performance. To tackle this issue, we propose a method called Nearest Neighbor Matching (NNM) to match samples with their nearest neighbors from both local (batch) and global (overall) levels. Specifically, for the local level, we match the nearest neighbors based on batch embedded features, as for the global one, we match neighbors from overall embedded features. To keep the clustering assignment consistent in both neighbors and classes, we frame consistent loss and class contrastive loss for both local and global levels. Experimental results on three benchmark datasets demonstrate the superiority of our new model against state-of-the-art methods. Particularly on the STL-10 dataset, our method can achieve supervised performance. As for the CIFAR-100 dataset, our NNM leads 3.7% against the latest comparison method. Our code will be available at https://github.com/ZhiyuanDang/NNM.

Classical subspace clustering methods often assume that the raw form data lie in a union of the low-dimension linear subspace. This assumption is too strict in practice, which largely limits the generalization of subspace clustering. To tackle this issue, deep subspace clustering (DSC) networks based on deep autoencoder (DAE) have been proposed, which non-linearly map the raw form data into a latent space well-adapted to subspace clustering. However, existing DSC models ignore the important multi-scale information embedded in DAE, thus abandon the much more useful deep features, leading their suboptimal clustering results. In this paper, we propose the Multi-Scale Fusion Subspace Clustering Using Similarity Constraint (SC-MSFSC) network, which learns a more discriminative self-expression coefficient matrix by a novel multi-scale fusion module. More importantly, it introduces a similarity constraint module to guide the fused self-expression coefficient matrix in training. Specifically, the multi-scale fusion module is framed to generate the self-expression coefficient matrix of each convolutional layer in DAE and then fuses them with the convolutional kernel. In addition, the similarity constraint module is to supervise the fused self-expression coefficient matrix by the designed similarity matrix. Extensive experimental results on four benchmark datasets demonstrate the superiority of our new model against state-of-the-art methods.

In a lot of real-world data mining and machine learning applications, data are provided by multiple providers and each maintains private records of different feature sets about common entities. It is challenging to train these vertically partitioned data effectively and efficiently while keeping data privacy for traditional data mining and machine learning algorithms. In this paper, we focus on nonlinear learning with kernels,and propose a federated doubly stochastic kernel learning (FDSKL) algorithm for vertically partitioned data. Specifically, we use random features to approximate the kernel mapping function and use doubly stochastic gradients to update the solutions, which are all computed federatedly without the disclosure of data. Importantly, we prove that FDSKL has a sublinear convergence rate, and can guarantee the data security under the semi-honest assumption. Extensive experimental results on a variety of benchmark datasets show that FDSKL is significantly faster than state-of-the-art federated learning methods when dealing with kernels, while retaining the similar generalization performance.