arXiv subjects

Wu-Jun Li

Publications and source records attributed to Wu-Jun Li.

At least 55 records · Page 3Linked to original sources

arXiv2019

On the Convergence of Memory-Based Distributed SGD

Distributed stochastic gradient descent~(DSGD) has been widely used for optimizing large-scale machine learning models, including both convex and non-convex models. With the rapid growth of model size, huge communication cost has been the bottleneck of traditional DSGD. Recently, many communication compression methods have been proposed. Memory-based distributed stochastic gradient descent~(M-DSGD) is one of the efficient methods since each worker communicates a sparse vector in each iteration so that the communication cost is small. Recent works propose the convergence rate of M-DSGD when it adopts vanilla SGD. However, there is still a lack of convergence theory for M-DSGD when it adopts momentum SGD. In this paper, we propose a universal convergence analysis for M-DSGD by introducing \emph{transformation equation}. The transformation equation describes the relation between traditional DSGD and M-DSGD so that we can transform M-DSGD to its corresponding DSGD. Hence we get the convergence rate of M-DSGD with momentum for both convex and non-convex problems. Furthermore, we combine M-DSGD and stagewise learning that the learning rate of M-DSGD in each stage is a constant and is decreased by stage, instead of iteration. Using the transformation equation, we propose the convergence rate of stagewise M-DSGD which bridges the gap between theory and practice.

stat.ML↗

arXiv2019

Convolutional Geometric Matrix Completion

Geometric matrix completion (GMC) has been proposed for recommendation by integrating the relationship (link) graphs among users/items into matrix completion (MC). Traditional GMC methods typically adopt graph regularization to impose smoothness priors for MC. Recently, geometric deep learning on graphs (GDLG) is proposed to solve the GMC problem, showing better performance than existing GMC methods including traditional graph regularization based methods. To the best of our knowledge, there exists only one GDLG method for GMC, which is called RMGCNN. RMGCNN combines graph convolutional network (GCN) and recurrent neural network (RNN) together for GMC. In the original work of RMGCNN, RMGCNN demonstrates better performance than pure GCN-based method. In this paper, we propose a new GMC method, called convolutional geometric matrix completion (CGMC), for recommendation with graphs among users/items. CGMC is a pure GCN-based method with a newly designed graph convolutional network. Experimental results on real datasets show that CGMC can outperform other state-of-the-art methods including RMGCNN in terms of both accuracy and speed.

cs.LG↗

arXiv2019

Deep Multi-Index Hashing for Person Re-Identification

Traditional person re-identification (ReID) methods typically represent person images as real-valued features, which makes ReID inefficient when the gallery set is extremely large. Recently, some hashing methods have been proposed to make ReID more efficient. However, these hashing methods will deteriorate the accuracy in general, and the efficiency of them is still not high enough. In this paper, we propose a novel hashing method, called deep multi-index hashing (DMIH), to improve both efficiency and accuracy for ReID. DMIH seamlessly integrates multi-index hashing and multi-branch based networks into the same framework. Furthermore, a novel block-wise multi-index hashing table construction approach and a search-aware multi-index (SAMI) loss are proposed in DMIH to improve the search efficiency. Experiments on three widely used datasets show that DMIH can outperform other state-of-the-art baselines, including both hashing methods and real-valued methods, in terms of both efficiency and accuracy.

cs.CV↗

arXiv2019

Hashing based Answer Selection

Answer selection is an important subtask of question answering (QA), where deep models usually achieve better performance. Most deep models adopt question-answer interaction mechanisms, such as attention, to get vector representations for answers. When these interaction based deep models are deployed for online prediction, the representations of all answers need to be recalculated for each question. This procedure is time-consuming for deep models with complex encoders like BERT which usually have better accuracy than simple encoders. One possible solution is to store the matrix representation (encoder output) of each answer in memory to avoid recalculation. But this will bring large memory cost. In this paper, we propose a novel method, called hashing based answer selection (HAS), to tackle this problem. HAS adopts a hashing strategy to learn a binary matrix representation for each answer, which can dramatically reduce the memory cost for storing the matrix representations of answers. Hence, HAS can adopt complex encoders like BERT in the model, but the online prediction of HAS is still fast with a low memory cost. Experimental results on three popular answer selection datasets show that HAS can outperform existing models to achieve state-of-the-art performance.

cs.CL↗

arXiv2019

Gated Group Self-Attention for Answer Selection

Answer selection (answer ranking) is one of the key steps in many kinds of question answering (QA) applications, where deep models have achieved state-of-the-art performance. Among these deep models, recurrent neural network (RNN) based models are most popular, typically with better performance than convolutional neural network (CNN) based models. Nevertheless, it is difficult for RNN based models to capture the information about long-range dependency among words in the sentences of questions and answers. In this paper, we propose a new deep model, called gated group self-attention (GGSA), for answer selection. GGSA is inspired by global self-attention which is originally proposed for machine translation and has not been explored in answer selection. GGSA tackles the problem of global self-attention that local and global information cannot be well distinguished. Furthermore, an interaction mechanism between questions and answers is also proposed to enhance GGSA by a residual structure. Experimental results on two popular QA datasets show that GGSA can outperform existing answer selection models to achieve state-of-the-art performance. Furthermore, GGSA can also achieve higher accuracy than global self-attention for the answer selection task, with a lower computation cost.

cs.CL↗

arXiv2019

Robust Frequent Directions with Application in Online Learning

The frequent directions (FD) technique is a deterministic approach for online sketching that has many applications in machine learning. The conventional FD is a heuristic procedure that often outputs rank deficient matrices. To overcome the rank deficiency problem, we propose a new sketching strategy called robust frequent directions (RFD) by introducing a regularization term. RFD can be derived from an optimization problem. It updates the sketch matrix and the regularization term adaptively and jointly. RFD reduces the approximation error of FD without increasing the computational cost. We also apply RFD to online learning and propose an effective hyperparameter-free online Newton algorithm. We derive a regret bound for our online Newton algorithm based on RFD, which guarantees the robustness of the algorithm. The experimental studies demonstrate that the proposed method outperforms state-of-the-art second order online learning algorithms.

cs.LG↗

arXiv2019

Quantized Epoch-SGD for Communication-Efficient Distributed Learning

Due to its efficiency and ease to implement, stochastic gradient descent (SGD) has been widely used in machine learning. In particular, SGD is one of the most popular optimization methods for distributed learning. Recently, quantized SGD (QSGD), which adopts quantization to reduce the communication cost in SGD-based distributed learning, has attracted much attention. Although several QSGD methods have been proposed, some of them are heuristic without theoretical guarantee, and others have high quantization variance which makes the convergence become slow. In this paper, we propose a new method, called Quantized Epoch-SGD (QESGD), for communication-efficient distributed learning. QESGD compresses (quantizes) the parameter with variance reduction, so that it can get almost the same performance as that of SGD with less communication cost. QESGD is implemented on the Parameter Server framework, and empirical results on distributed deep learning show that QESGD can outperform other state-of-the-art quantization methods to achieve the best performance.

cs.LG↗

arXiv2018

Proximal SCOPE for Distributed Sparse Learning: Better Data Partition Implies Faster Convergence Rate

Distributed sparse learning with a cluster of multiple machines has attracted much attention in machine learning, especially for large-scale applications with high-dimensional data. One popular way to implement sparse learning is to use $L_1$ regularization. In this paper, we propose a novel method, called proximal \mbox{SCOPE}~(\mbox{pSCOPE}), for distributed sparse learning with $L_1$ regularization. pSCOPE is based on a \underline{c}ooperative \underline{a}utonomous \underline{l}ocal \underline{l}earning~(\mbox{CALL}) framework. In the \mbox{CALL} framework of \mbox{pSCOPE}, we find that the data partition affects the convergence of the learning procedure, and subsequently we define a metric to measure the goodness of a data partition. Based on the defined metric, we theoretically prove that pSCOPE is convergent with a linear convergence rate if the data partition is good enough. We also prove that better data partition implies faster convergence rate. Furthermore, pSCOPE is also communication efficient. Experimental results on real data sets show that pSCOPE can outperform other state-of-the-art distributed methods for sparse learning.

stat.ML↗

arXiv2018

Feature-Distributed SVRG for High-Dimensional Linear Classification

Linear classification has been widely used in many high-dimensional applications like text classification. To perform linear classification for large-scale tasks, we often need to design distributed learning methods on a cluster of multiple machines. In this paper, we propose a new distributed learning method, called feature-distributed stochastic variance reduced gradient (FD-SVRG) for high-dimensional linear classification. Unlike most existing distributed learning methods which are instance-distributed, FD-SVRG is feature-distributed. FD-SVRG has lower communication cost than other instance-distributed methods when the data dimensionality is larger than the number of data instances. Experimental results on real data demonstrate that FD-SVRG can outperform other state-of-the-art distributed methods for high-dimensional linear classification in terms of both communication cost and wall-clock time, when the dimensionality is larger than the number of instances in training data.

cs.LG↗

arXiv2017

Deep Discrete Supervised Hashing

Hashing has been widely used for large-scale search due to its low storage cost and fast query speed. By using supervised information, supervised hashing can significantly outperform unsupervised hashing. Recently, discrete supervised hashing and deep hashing are two representative progresses in supervised hashing. On one hand, hashing is essentially a discrete optimization problem. Hence, utilizing supervised information to directly guide discrete (binary) coding procedure can avoid sub-optimal solution and improve the accuracy. On the other hand, deep hashing, which integrates deep feature learning and hash-code learning into an end-to-end architecture, can enhance the feedback between feature learning and hash-code learning. The key in discrete supervised hashing is to adopt supervised information to directly guide the discrete coding procedure in hashing. The key in deep hashing is to adopt the supervised information to directly guide the deep feature learning procedure. However, there have not existed works which can use the supervised information to directly guide both discrete coding procedure and deep feature learning procedure in the same framework. In this paper, we propose a novel deep hashing method, called deep discrete supervised hashing (DDSH), to address this problem. DDSH is the first deep hashing method which can utilize supervised information to directly guide both discrete coding procedure and deep feature learning procedure, and thus enhance the feedback between these two important procedures. Experiments on three real datasets show that DDSH can outperform other state-of-the-art baselines, including both discrete hashing and deep hashing baselines, for image retrieval.

cs.IR↗

arXiv2017

Discrete Latent Factor Model for Cross-Modal Hashing

Due to its storage and retrieval efficiency, cross-modal hashing~(CMH) has been widely used for cross-modal similarity search in multimedia applications. According to the training strategy, existing CMH methods can be mainly divided into two categories: relaxation-based continuous methods and discrete methods. In general, the training of relaxation-based continuous methods is faster than discrete methods, but the accuracy of relaxation-based continuous methods is not satisfactory. On the contrary, the accuracy of discrete methods is typically better than relaxation-based continuous methods, but the training of discrete methods is time-consuming. In this paper, we propose a novel CMH method, called discrete latent factor model based cross-modal hashing~(DLFH), for cross modal similarity search. DLFH is a discrete method which can directly learn the binary hash codes for CMH. At the same time, the training of DLFH is efficient. Experiments on real datasets show that DLFH can achieve significantly better accuracy than existing methods, and the training time of DLFH is comparable to that of relaxation-based continuous methods which are much faster than existing discrete methods.

cs.IR↗

arXiv2017

Asymmetric Deep Supervised Hashing

Hashing has been widely used for large-scale approximate nearest neighbor search because of its storage and search efficiency. Recent work has found that deep supervised hashing can significantly outperform non-deep supervised hashing in many applications. However, most existing deep supervised hashing methods adopt a symmetric strategy to learn one deep hash function for both query points and database (retrieval) points. The training of these symmetric deep supervised hashing methods is typically time-consuming, which makes them hard to effectively utilize the supervised information for cases with large-scale database. In this paper, we propose a novel deep supervised hashing method, called asymmetric deep supervised hashing (ADSH), for large-scale nearest neighbor search. ADSH treats the query points and database points in an asymmetric way. More specifically, ADSH learns a deep hash function only for query points, while the hash codes for database points are directly learned. The training of ADSH is much more efficient than that of traditional symmetric deep supervised hashing methods. Experiments show that ADSH can achieve state-of-the-art performance in real applications.

cs.LG↗

arXiv2017

ParaGraphE: A Library for Parallel Knowledge Graph Embedding

Knowledge graph embedding aims at translating the knowledge graph into numerical representations by transforming the entities and relations into continuous low-dimensional vectors. Recently, many methods [1, 5, 3, 2, 6] have been proposed to deal with this problem, but existing single-thread implementations of them are time-consuming for large-scale knowledge graphs. Here, we design a unified parallel framework to parallelize these methods, which achieves a significant time reduction without influencing the accuracy. We name our framework as ParaGraphE, which provides a library for parallel knowledge graph embedding. The source code can be downloaded from https://github.com/LIBBLE/LIBBLE-MultiThread/tree/master/ParaGraphE .

cs.AI↗

arXiv2016

SCOPE: Scalable Composite Optimization for Learning on Spark

Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to solve the large-scale composite optimization problems, which have shown better performance than traditional batch methods. However, most of these DSO methods are not scalable enough. In this paper, we propose a novel DSO method, called \underline{s}calable \underline{c}omposite \underline{op}timization for l\underline{e}arning~({SCOPE}), and implement it on the fault-tolerant distributed platform \mbox{Spark}. SCOPE is both computation-efficient and communication-efficient. Theoretical analysis shows that SCOPE is convergent with linear convergence rate when the objective function is convex. Furthermore, empirical results on real datasets show that SCOPE can outperform other state-of-the-art distributed learning methods on Spark, including both batch learning methods and DSO methods.

stat.ML↗

arXiv2016

Lock-Free Optimization for Non-Convex Problems

Stochastic gradient descent~(SGD) and its variants have attracted much attention in machine learning due to their efficiency and effectiveness for optimization. To handle large-scale problems, researchers have recently proposed several lock-free strategy based parallel SGD~(LF-PSGD) methods for multi-core systems. However, existing works have only proved the convergence of these LF-PSGD methods for convex problems. To the best of our knowledge, no work has proved the convergence of the LF-PSGD methods for non-convex problems. In this paper, we provide the theoretical proof about the convergence of two representative LF-PSGD methods, Hogwild! and AsySVRG, for non-convex problems. Empirical results also show that both Hogwild! and AsySVRG are convergent on non-convex problems, which successfully verifies our theoretical results.

stat.ML↗

arXiv2016

A Proximal Stochastic Quasi-Newton Algorithm

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and the non-smooth part is equipped with a simple proximal mapping. We propose a proximal stochastic second-order method, which is efficient and scalable. It incorporates the Hessian in the smooth part of the function and exploits multistage scheme to reduce the variance of the stochastic gradient. We prove that our method can achieve linear rate of convergence.

cs.LG↗

arXiv2016

Full-Time Supervision based Bidirectional RNN for Factoid Question Answering

Recently, bidirectional recurrent neural network (BRNN) has been widely used for question answering (QA) tasks with promising performance. However, most existing BRNN models extract the information of questions and answers by directly using a pooling operation to generate the representation for loss or similarity calculation. Hence, these existing models don't put supervision (loss or similarity calculation) at every time step, which will lose some useful information. In this paper, we propose a novel BRNN model called full-time supervision based BRNN (FTS-BRNN), which can put supervision at every time step. Experiments on the factoid QA task show that our FTS-BRNN can outperform other baselines to achieve the state-of-the-art accuracy.

cs.CL↗

arXiv2016

Feature Learning based Deep Supervised Hashing with Pairwise Labels

Recent years have witnessed wide application of hashing for large-scale image retrieval. However, most existing hashing methods are based on hand-crafted features which might not be optimally compatible with the hashing procedure. Recently, deep hashing methods have been proposed to perform simultaneous feature learning and hash-code learning with deep neural networks, which have shown better performance than traditional hashing methods with hand-crafted features. Most of these deep hashing methods are supervised whose supervised information is given with triplet labels. For another common application scenario with pairwise labels, there have not existed methods for simultaneous feature learning and hash-code learning. In this paper, we propose a novel deep hashing method, called deep pairwise-supervised hashing(DPSH), to perform simultaneous feature learning and hash-code learning for applications with pairwise labels. Experiments on real datasets show that our DPSH method can outperform other methods to achieve the state-of-the-art performance in image retrieval applications.

cs.LG↗