Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

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Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

We present Resilient Distributed Datasets (RDDs), a distributed memory abstraction that lets programmers perform in-memory computations on large clusters in a fault-tolerant manner. RDDs are motivated by two types of applications that current computing frameworks handle inefficiently: iterative algorithms and interactive data mining tools. In both cases, keeping data in memory can improve performance by an order of magnitude. To achieve fault tolerance efficiently, RDDs provide a restricted form of shared memory, based on coarse-grained transformations rather than fine-grained updates to shared state. However, we show that RDDs are expressive enough to capture a wide class of computations, including recent specialized programming models for iterative jobs, such as Pregel, and new applications that these models do not capture. We have implemented RDDs in a system called Spark, which we evaluate through a variety of user applications and benchmarks.

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Resilient distributed datasets: a fault-tolerant abstraction for in-memory cluster computing

In this paper, we review the background and state-of-the-art of big data. We first introduce the general background of big data and review related technologies, such as could computing, Internet of Things, data centers, and Hadoop. We then focus on the four phases of the value chain of big data, i.e., data generation, data acquisition, data storage, and data analysis. For each phase, we introduce the general background, discuss the technical challenges, and review the latest advances. We finally examine the several representative applications of big data, including enterprise management, Internet of Things, online social networks, medial applications, collective intelligence, and smart grid. These discussions aim to provide a comprehensive overview and big-picture to readers of this exciting area. This survey is concluded with a discussion of open problems and future directions.

Big Data: A Survey

The initial design of Apache Hadoop [1] was tightly focused on running massive, MapReduce jobs to process a web crawl. For increasingly diverse companies, Hadoop has become the data and computational agora---the de facto place where data and computational resources are shared and accessed. This broad adoption and ubiquitous usage has stretched the initial design well beyond its intended target, exposing two key shortcomings: 1) tight coupling of a specific programming model with the resource management infrastructure, forcing developers to abuse the MapReduce programming model, and 2) centralized handling of jobs' control flow, which resulted in endless scalability concerns for the scheduler. In this paper, we summarize the design, development, and current state of deployment of the next generation of Hadoop's compute platform: YARN. The new architecture we introduced decouples the programming model from the resource management infrastructure, and delegates many scheduling functions (e.g., task fault-tolerance) to per-application components. We provide experimental evidence demonstrating the improvements we made, confirm improved efficiency by reporting the experience of running YARN on production environments (including 100% of Yahoo! grids), and confirm the flexibility claims by discussing the porting of several programming frameworks onto YARN viz. Dryad, Giraph, Hoya, Hadoop MapReduce, REEF, Spark, Storm, Tez.

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Apache Hadoop YARN: yet another resource negotiator

The popularity of the Web and Internet commerce provides many extremely large datasets from which information can be gleaned by data mining. This book focuses on practical algorithms that have been used to solve key problems in data mining and which can be used on even the largest datasets. It begins with a discussion of the map-reduce framework, an important tool for parallelizing algorithms automatically. The authors explain the tricks of locality-sensitive hashing and stream processing algorithms for mining data that arrives too fast for exhaustive processing. The PageRank idea and related tricks for organizing the Web are covered next. Other chapters cover the problems of finding frequent itemsets and clustering. The final chapters cover two applications: recommendation systems and Web advertising, each vital in e-commerce. Written by two authorities in database and Web technologies, this book is essential reading for students and practitioners alike.

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Mining of Massive Datasets

Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs - in some cases billions of vertices, trillions of edges - poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertex-centric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and fault-tolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distribution-related details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.

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Pregel: a system for large-scale graph processing

Although users of online communication tools rarely categorize their contacts into groups such as "family", "co-workers", or "jogging buddies", they nonetheless implicitly cluster contacts, by virtue of their interactions with them, forming implicit groups. In this paper, we describe the implicit social graph which is formed by users' interactions with contacts and groups of contacts, and which is distinct from explicit social graphs in which users explicitly add other individuals as their "friends". We introduce an interaction-based metric for estimating a user's affinity to his contacts and groups. We then describe a novel friend suggestion algorithm that uses a user's implicit social graph to generate a friend group, given a small seed set of contacts which the user has already labeled as friends. We show experimental results that demonstrate the importance of both implicit group relationships and interaction-based affinity ranking in suggesting friends. Finally, we discuss two applications of the Friend Suggest algorithm that have been released as Gmail Labs features.

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Suggesting friends using the implicit social graph

Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertexcentric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and fault-tolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distributionrelated details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.

Pregel: a system for large-scale graph processing - "ABSTRACT"

A computer system having one or more processors and memory receives seed data comprising contacts specified for a draft communication, selects at least a subset of the seed data as a seed set of contacts, and identifies one or more suggested contacts based on the seed set. Identifying the suggested contacts includes: identifying in historical communications in a user account, groups of contacts that include one or more of the contacts in the seed set; generating scores for contacts in the identified groups of contacts, including generating a contact score for a respective contact by accumulating score contributions for a plurality of the identified groups of contacts that include the respective contact; and identifying the one or more suggested contacts in accordance with the generated scores. The computer system sends a contact suggestion based on the suggested contacts for display in conjunction with the draft communication.

Generating Contact Suggestions

Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. Despite the ubiquity of large graphs and their commercial importance, we know of no scalable general-purpose system for implementing graph algorithms in a distributed environment. To address distributed processing of real-life graphs, we defined a model of computation and realized it through a scalable and fault-tolerant system called Pregel, with an expressive and flexible API. The high-level organization of Pregel programs is inspired by Valiant’s Bulk Synchronous Parallel model. Pregel computations consist of a sequence of iterations, called superstep s. During a superstep the framework invokes a userdefined Compute() function for each vertex, conceptually in parallel. The function specifies behavior at a single vertex v and a single superstep S. It can read messages sent to v in superstep S − 1, send messages to other vertices that will be received at superstep S + 1, and modify the state of v and its outgoing edges. Messages are typically sent along outgoing edges, but a message may be sent to any vertex whose identifier is known. A program terminates when all vertices declare that they are done. The input and output are both directed graphs. They are often but not always isomorphic, because vertices and edges can be added and removed during computation. Userdefined handlers are applied to resolve conflicts for concurrent mutations. The vertex-centric flavor of programming in Pregel is similar to the MapReduce model in that programmers focus on a local action, processing a single item at a time, which the system then lifts to computation on a large dataset. The synchronicity of the Pregel model simplifies writing correct programs and simplifies reasoning about the inter-

Ilan Horn

Papers

Pregel: a system for large-scale graph processing

Suggesting friends using the implicit social graph

Pregel: a system for large-scale graph processing - "ABSTRACT"

Generating Contact Suggestions

Pregel: a system for large-scale graph processing - "ABSTRACT"