There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available. These areas include text processing of internet documents, gene expression array analysis, and combinatorial chemistry. The objective of variable selection is three-fold: improving the prediction performance of the predictors, providing faster and more cost-effective predictors, and providing a better understanding of the underlying process that generated the data. The contributions of this special issue cover a wide range of aspects of such problems: providing a better definition of the objective function, feature construction, feature ranking, multivariate feature selection, efficient search methods, and feature validity assessment methods.

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An introduction to variable and feature selection

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

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

With the widespread availability of video cameras, we are facing an ever-growing enormous collection of unedited and unstructured video data. Due to lack of an automatic way to generate highlights from this large collection of video streams, these videos can be tedious and time consuming to index or search. The present invention is a novel method of online video highlighting, a principled way of generating a short video highlight summarizing the most important and interesting contents of a potentially very long video, which is costly both time-wise and financially for manual processing. Specifically, the method learns a dictionary from given video using group sparse coding, and updates atoms in the dictionary on-the-fly. A highlight of the given video is then generated by combining segments that cannot be sparsely reconstructed using the learned dictionary. The online fashion of the method enables it to process arbitrarily long videos and starts generating highlights before seeing the end of the video, both attractive characteristics for practical applications.

System and method for processing a video stream to extract highlights

In this paper, a variant of a spectral clustering algorithm is proposed for bilingual word clustering. The proposed algorithm generates the two sets of clusters for both languages efficiently with high semantic correlation within monolingual clusters, and high translation quality across the clusters between two languages. Each cluster level translation is considered as a bilingual concept, which generalizes words in bilingual clusters. This scheme improves the robustness for statistical machine translation models. Two HMM-based translation models are tested to use these bilingual clusters. Improved perplexity, word alignment accuracy, and translation quality are observed in our experiments.

/pdf/bilingual-word-spectral-clustering-for-statistical-machine-2zuf6hi8to.pdf

Bilingual Word Spectral Clustering for Statistical Machine Translation

Many graph mining and analysis services have been deployed on the cloud, which can alleviate users from the burden of implementing and maintaining graph algorithms. However, putting graph analytics on the cloud can invade users' privacy. To solve this problem, we propose CryptGraph, which runs graph analytics on encrypted graph to preserve the privacy of both users' graph data and the analytic results. In CryptGraph, users encrypt their graphs before uploading them to the cloud. The cloud runs graph analysis on the encrypted graphs and obtains results which are also in encrypted form that the cloud cannot decipher. During the process of computing, the encrypted graphs are never decrypted on the cloud side. The encrypted results are sent back to users and users perform the decryption to obtain the plaintext results. In this process, users' graphs and the analytics results are both encrypted and the cloud knows neither of them. Thereby, users' privacy can be strongly protected. Meanwhile, with the help of homomorphic encryption, the results analyzed from the encrypted graphs are guaranteed to be correct. In this paper, we present how to encrypt a graph using homomorphic encryption and how to query the structure of an encrypted graph by computing polynomials. To solve the problem that certain operations are not executable on encrypted graphs, we propose hard computation outsourcing to seek help from users. Using two graph algorithms as examples, we show how to apply our methods to perform analytics on encrypted graphs. Experiments on two datasets demonstrate the correctness and feasibility of our methods.

CryptGraph: Privacy Preserving Graph Analytics on Encrypted Graph.

Brand Associations, one of central concepts in marketing, describe customers' top-of-mind attitudes or feelings toward a brand. Thus, this consumer-driven brand equity often attains the grounds for purchasing products or services of the brand. Traditionally, brand associations are measured by analyzing the text data from consumers' responses to the survey or their online conversation logs. In this paper, we propose to go beyond text data and leverage large-scale online photo collections contributed by the general public, which have not been explored so far. As a first technical step toward the study of photo-based brand associations, we aim to jointly achieve the following two visualization tasks in a mutually-rewarding way: (i) detecting and visualizing core visual concepts associated with brands, and (ii) localizing the regions of brand in the images. With experiments on about five millions of images of 48 brands crawled from five popular online photo sharing sites, we demonstrate that our approach can discover complementary views on the brand associations that are hardly mined from the text data. We also quantitatively show that our approach outperforms other candidate methods on the both visualization tasks.

https://dl.acm.org/doi/pdf/10.1145/2556195.2556212

Visualizing brand associations from web community photos

Association mapping studies promise to link DNA mutations to gene expression data, possibly leading to innovative treatments for diseases. One challenge in large-scale association mapping studies is exploring the results of the computational analysis to find relevant and interesting associations. Although many association mapping studies find associations from a genome-wide collection of genomic data to hundreds or thousands of traits, current visualization software only allow these associations to be explored one trait at a time. The inability to explore the association of a genomic location to multiple traits hides the inherent interaction between traits in the analysis. Additionally, researchers must rely on collections of in-house scripts and multiple tools to perform an analysis, adding time and effort to find interesting associations. In this paper, we present a novel visual analytics system called GenAMap. GenAMap replaces the time-consuming analysis of large-scale association mapping studies with exploratory visualization tools that give geneticists an overview of the data and lead them to relevant information. We present the results of a preliminary evaluation that validated our basic approach.

/pdf/genamap-visualization-strategies-for-structured-association-2i6pf8x9xx.pdf

Eric P. Xing

Papers

System and method for processing a video stream to extract highlights

Bilingual Word Spectral Clustering for Statistical Machine Translation

CryptGraph: Privacy Preserving Graph Analytics on Encrypted Graph.

Visualizing brand associations from web community photos

GenAMap: Visualization strategies for structured association mapping