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

Tree boosting is a highly effective and widely used machine learning method. In this paper, we describe a scalable end-to-end tree boosting system called XGBoost, which is used widely by data scientists to achieve state-of-the-art results on many machine learning challenges. We propose a novel sparsity-aware algorithm for sparse data and weighted quantile sketch for approximate tree learning. More importantly, we provide insights on cache access patterns, data compression and sharding to build a scalable tree boosting system. By combining these insights, XGBoost scales beyond billions of examples using far fewer resources than existing systems.

/pdf/xgboost-a-scalable-tree-boosting-system-48ocu6x4c7.pdf

XGBoost: A Scalable Tree Boosting System

TensorFlow is a machine learning system that operates at large scale and in heterogeneous environments. Tensor-Flow uses dataflow graphs to represent computation, shared state, and the operations that mutate that state. It maps the nodes of a dataflow graph across many machines in a cluster, and within a machine across multiple computational devices, including multicore CPUs, general-purpose GPUs, and custom-designed ASICs known as Tensor Processing Units (TPUs). This architecture gives flexibility to the application developer: whereas in previous "parameter server" designs the management of shared state is built into the system, TensorFlow enables developers to experiment with novel optimizations and training algorithms. TensorFlow supports a variety of applications, with a focus on training and inference on deep neural networks. Several Google services use TensorFlow in production, we have released it as an open-source project, and it has become widely used for machine learning research. In this paper, we describe the TensorFlow dataflow model and demonstrate the compelling performance that TensorFlow achieves for several real-world applications.

/pdf/tensorflow-a-system-for-large-scale-machine-learning-10wgdjhl6k.pdf

TensorFlow: a system for large-scale machine learning

TensorFlow is an interface for expressing machine learning algorithms, and an
implementation for executing such algorithms. A computation expressed using
TensorFlow can be executed with little or no change on a wide variety of
heterogeneous systems, ranging from mobile devices such as phones and tablets
up to large-scale distributed systems of hundreds of machines and thousands of
computational devices such as GPU cards. The system is flexible and can be used
to express a wide variety of algorithms, including training and inference
algorithms for deep neural network models, and it has been used for conducting
research and for deploying machine learning systems into production across more
than a dozen areas of computer science and other fields, including speech
recognition, computer vision, robotics, information retrieval, natural language
processing, geographic information extraction, and computational drug
discovery. This paper describes the TensorFlow interface and an implementation
of that interface that we have built at Google. The TensorFlow API and a
reference implementation were released as an open-source package under the
Apache 2.0 license in November, 2015 and are available at www.tensorflow.org.

/pdf/tensorflow-large-scale-machine-learning-on-heterogeneous-2yk4fgchw6.pdf

TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems

Clearing the clouds away from the true potential and obstacles posed by this computing capability.

https://dl.acm.org/doi/pdf/10.1145/1721654.1721672

A view of cloud computing

Cloud Computing, the long-held dream of computing as a utility, has the potential to transform a large part of the IT industry, making software even more attractive as a service and shaping the way IT hardware is designed and purchased. Developers with innovative ideas for new Internet services no longer require the large capital outlays in hardware to deploy their service or the human expense to operate it. They need not be concerned about overprovisioning for a service whose popularity does not meet their predictions, thus wasting costly resources, or underprovisioning for one that becomes wildly popular, thus missing potential customers and revenue. Moreover, companies with large batch-oriented tasks can get results as quickly as their programs can scale, since using 1000 servers for one hour costs no more than using one server for 1000 hours. This elasticity of resources, without paying a premium for large scale, is unprecedented in the history of IT. Cloud Computing refers to both the applications delivered as services over the Internet and the hardware and systems software in the datacenters that provide those services. The services themselves have long been referred to as Software as a Service (SaaS). The datacenter hardware and software is what we will call a Cloud. When a Cloud is made available in a pay-as-you-go manner to the general public, we call it a Public Cloud; the service being sold is Utility Computing. We use the term Private Cloud to refer to internal datacenters of a business or other organization, not made available to the general public. Thus, Cloud Computing is the sum of SaaS and Utility Computing, but does not include Private Clouds. People can be users or providers of SaaS, or users or providers of Utility Computing. We focus on SaaS Providers (Cloud Users) and Cloud Providers, which have received less attention than SaaS Users. From a hardware point of view, three aspects are new in Cloud Computing.

/pdf/above-the-clouds-a-berkeley-view-of-cloud-computing-tkj3etim13.pdf

Above the Clouds: A Berkeley View of Cloud Computing

MapReduce and its variants have been highly successful in implementing large-scale data-intensive applications on commodity clusters. However, most of these systems are built around an acyclic data flow model that is not suitable for other popular applications. This paper focuses on one such class of applications: those that reuse a working set of data across multiple parallel operations. This includes many iterative machine learning algorithms, as well as interactive data analysis tools. We propose a new framework called Spark that supports these applications while retaining the scalability and fault tolerance of MapReduce. To achieve these goals, Spark introduces an abstraction called resilient distributed datasets (RDDs). An RDD is a read-only collection of objects partitioned across a set of machines that can be rebuilt if a partition is lost. Spark can outperform Hadoop by 10x in iterative machine learning jobs, and can be used to interactively query a 39 GB dataset with sub-second response time.

/pdf/spark-cluster-computing-with-working-sets-2mqxkxxuqt.pdf

Spark: cluster computing with working sets

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.

/pdf/resilient-distributed-datasets-a-fault-tolerant-abstraction-1jmy0nuhco.pdf

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

MapReduce is emerging as an important programming model for large-scale data-parallel applications such as web indexing, data mining, and scientific simulation. Hadoop is an open-source implementation of MapReduce enjoying wide adoption and is often used for short jobs where low response time is critical. Hadoop's performance is closely tied to its task scheduler, which implicitly assumes that cluster nodes are homogeneous and tasks make progress linearly, and uses these assumptions to decide when to speculatively re-execute tasks that appear to be stragglers. In practice, the homogeneity assumptions do not always hold. An especially compelling setting where this occurs is a virtualized data center, such as Amazon's Elastic Compute Cloud (EC2). We show that Hadoop's scheduler can cause severe performance degradation in heterogeneous environments. We design a new scheduling algorithm, Longest Approximate Time to End (LATE), that is highly robust to heterogeneity. LATE can improve Hadoop response times by a factor of 2 in clusters of 200 virtual machines on EC2.

/pdf/improving-mapreduce-performance-in-heterogeneous-49jm9yzum1.pdf

Matei Zaharia

Papers

A view of cloud computing

Above the Clouds: A Berkeley View of Cloud Computing

Spark: cluster computing with working sets

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

Improving MapReduce performance in heterogeneous environments