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

Game Theoretic Approaches to Massive Data Processing in Wireless Networks

Wireless communication networks are becoming highly virtualized with two-layer hierarchies, in which controllers at the upper layer with tasks to achieve can ask a large number of agents at the lower layer to help realize computation, storage, and transmission functions. Through offloading data processing to the agents, the controllers can accomplish otherwise prohibitive big data processing. Incentive mechanisms are needed for the agents to perform the controllers' tasks in order to satisfy the corresponding objectives of controllers and agents. In this article, a hierarchical game framework with fast convergence and scalability is proposed to meet the demand for real-time processing for such situations. Possible future research directions in this emerging area are also discussed

L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework

Despite the importance of sparsity in many large-scale applications, there are few methods for distributed optimization of sparsity-inducing objectives. In this paper, we present a communication-efficient framework for L1-regularized optimization in the distributed environment. By viewing classical objectives in a more general primal-dual setting, we develop a new class of methods that can be efficiently distributed and applied to common sparsity-inducing models, such as Lasso, sparse logistic regression, and elastic net-regularized problems. We provide theoretical convergence guarantees for our framework, and demonstrate its efficiency and flexibility with a thorough experimental comparison on Amazon EC2. Our proposed framework yields speedups of up to 50x as compared to current state-of-the-art methods for distributed L1-regularized optimization

Tensor Learning for Recovering Missing Information: Algorithms and Applications on Social Media

Real-time social systems like Facebook, Twitter, and Snapchat have been growing rapidly, producing exabytes of data in different views or aspects. Coupled with more and more GPS-enabled sharing of videos, images, blogs, and tweets that provide valuable information regarding “who”, “where”, “when” and “what”, these real-time human sensor data promise new research opportunities to uncover models of user behavior, mobility, and information sharing. These real-time dynamics in social systems usually come in multiple aspects, which are able to help better understand the social interactions of the underlying network. However, these multi-aspect datasets are often raw and incomplete owing to various unpredictable or unavoidable reasons; for instance, API limitations and data sampling policies can lead to an incomplete (and often biased) perspective on these multi-aspect datasets. This missing data could raise serious concerns such as biased estimations on structural properties of the network and properties of information cascades in social networks. In order to recover missing values or information in social systems, we identify “4S” challenges: extreme sparsity of the observed multi-aspect datasets, adoption of rich side information that is able to describe the similarities of entities, generation of robust models rather than limiting them on specific applications, and scalability of models to handle real large-scale datasets (billions of observed entries). With these challenges in mind, this dissertation aims to develop scalable and interpretable tensor-based frameworks, algorithms and methods for recovering missing information on social media. In particular, this dissertation research makes four unique contributions: _ The first research contribution of this dissertation research is to propose a scalable framework based on low-rank tensor learning in the presence of incomplete information. Concretely, we formally define the problem of recovering the spatio-temporal dynamics of online memes and tackle this problem by proposing a novel tensor-based factorization approach based on the alternative direction method of multipliers (ADMM) with the integration of the latent relationships derived from contextual information among locations, memes, and times. _ The second research contribution of this dissertation research is to evaluate the generalization of the proposed tensor learning framework and extend it to the recommendation problem. In particular, we develop a novel tensor-based approach to solve the personalized expert recommendation by integrating both the latent relationships between homogeneous entities (e.g., users and users, experts and experts) and the relationships between heterogeneous entities (e.g., users and experts, topics and experts) from the geo-spatial, topical, and social contexts. _ The third research contribution of this dissertation research is to extend the proposed tensor learning framework to the user topical profiling problem. Specifically, we propose a tensor-based contextual regularization model embedded into a matrix factorization framework, which leverages the social, textual, and behavioral contexts across users, in order to overcome identified challenges. _ The fourth research contribution of this dissertation research is to scale up the proposed tensor learning framework to be capable of handling real large-scale datasets that are too big to fit in the main memory of a single machine. Particularly, we propose a novel distributed tensor completion algorithm with the trace-based regularization of the auxiliary information based on ADMM under the proposed tensor learning framework, which is designed to scale up to real large-scale tensors (e.g., billions of entries) by efficiently computing auxiliary variables, minimizing intermediate data, and reducing the workload of updating new tensors