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.

/pdf/distributed-optimization-and-statistical-learning-via-the-8s9gtddw0d.pdf

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.

/pdf/an-introduction-to-variable-and-feature-selection-22eu49r0zd.pdf

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

We introduce Texar, an open-source toolkit aiming to support the broad set of text generation tasks that transform any inputs into natural language, such as machine translation, summarization, dialog, content manipulation, and so forth With the design goals of modularity, versatility, and extensibility in mind, Texar extracts common patterns underlying the diverse tasks and methodologies, creates a library of highly reusable modules, and allows arbitrary model architectures and algorithmic paradigms In Texar, model architecture, inference, and learning processes are properly decomposed Modules at a high concept level can be freely assembled and plugged in/swapped out The toolkit also supports a rich set of large-scale pretrained models Texar is thus particularly suitable for researchers and practitioners to do fast prototyping and experimentation The versatile toolkit also fosters technique sharing across different text generation tasks Texar supports both TensorFlow and PyTorch, and is released under Apache License 20 at this https URL

Texar: A Modularized, Versatile, and Extensible Toolkit for Text Generation

Distance metric learning (DML), which learns a distance metric from labeled "similar" and "dissimilar" data pairs, is widely utilized. Recently, several works investigate orthogonality-promoting regularization (OPR), which encourages the projection vectors in DML to be close to being orthogonal, to achieve three effects: (1) high balancedness -- achieving comparable performance on both frequent and infrequent classes; (2) high compactness -- using a small number of projection vectors to achieve a "good" metric; (3) good generalizability -- alleviating overfitting to training data. While showing promising results, these approaches suffer three problems. First, they involve solving non-convex optimization problems where achieving the global optimal is NP-hard. Second, it lacks a theoretical understanding why OPR can lead to balancedness. Third, the current generalization error analysis of OPR is not directly on the regularizer. In this paper, we address these three issues by (1) seeking convex relaxations of the original nonconvex problems so that the global optimal is guaranteed to be achievable; (2) providing a formal analysis on OPR's capability of promoting balancedness; (3) providing a theoretical analysis that directly reveals the relationship between OPR and generalization performance. Experiments on various datasets demonstrate that our convex methods are more effective in promoting balancedness, compactness, and generalization, and are computationally more efficient, compared with the nonconvex methods.

/pdf/orthogonality-promoting-distance-metric-learning-convex-xj6fyh574m.pdf

Orthogonality-Promoting Distance Metric Learning: Convex Relaxation and Theoretical Analysis

We study the problem of alleviating the instability issue in the GAN training procedure via new architecture design. The discrepancy between the minimax and maximin objective values could serve as a proxy for the difficulties that the alternating gradient descent encounters in the optimization of GANs. In this work, we give new results on the benefits of multi-generator architecture of GANs. We show that the minimax gap shrinks to $\epsilon$ as the number of generators increases with rate $\widetilde{O}(1/\epsilon)$. This improves over the best-known result of $\widetilde{O}(1/\epsilon^2)$. At the core of our techniques is a novel application of Shapley-Folkman lemma to the generic minimax problem, where in the literature the technique was only known to work when the objective function is restricted to the Lagrangian function of a constraint optimization problem. Our proposed Stackelberg GAN performs well experimentally in both synthetic and real-world datasets, improving Fr\'echet Inception Distance by $14.61\%$ over the previous multi-generator GANs on the benchmark datasets.

/pdf/stackelberg-gan-towards-provable-minimax-equilibrium-via-16725xdjq1.pdf

Stackelberg GAN: Towards Provable Minimax Equilibrium via Multi-Generator Architectures

Reading comprehension (RC), aiming to understand natural texts and answer questions therein, is a challenging task. In this paper, we study the RC problem on the Stanford Question Answering Dataset (SQuAD). Observing from the training set that most correct answers are centered around constituents in the parse tree, we design a constituent-centric neural architecture where the generation of candidate answers and their representation learning are both based on constituents and guided by the parse tree. Under this architecture, the search space of candidate answers can be greatly reduced without sacrificing the coverage of correct answers and the syntactic, hierarchical and compositional structure among constituents can be well captured, which contributes to better representation learning of the candidate answers. On SQuAD, our method achieves the state of the art performance and the ablation study corroborates the effectiveness of individual modules.

/pdf/a-constituent-centric-neural-architecture-for-reading-rs2npyqcz2.pdf

A Constituent-Centric Neural Architecture for Reading Comprehension.

Machine learning (ML) training algorithms often possess an inherent self-correcting behavior due to their iterative-convergent nature. Recent systems exploit this property to achieve adaptability and efficiency in unreliable computing environments by relaxing the consistency of execution and allowing calculation errors to be self-corrected during training. However, the behavior of such systems are only well understood for specific types of calculation errors, such as those caused by staleness, reduced precision, or asynchronicity, and for specific types of training algorithms, such as stochastic gradient descent. In this paper, we develop a general framework to quantify the effects of calculation errors on iterative-convergent algorithms and use this framework to design new strategies for checkpoint-based fault tolerance. Our framework yields a worst-case upper bound on the iteration cost of arbitrary perturbations to model parameters during training. Our system, SCAR, employs strategies which reduce the iteration cost upper bound due to perturbations incurred when recovering from checkpoints. We show that SCAR can reduce the iteration cost of partial failures by 78% - 95% when compared with traditional checkpoint-based fault tolerance across a variety of ML models and training algorithms.

Eric P. Xing

Papers

Texar: A Modularized, Versatile, and Extensible Toolkit for Text Generation

Orthogonality-Promoting Distance Metric Learning: Convex Relaxation and Theoretical Analysis

Stackelberg GAN: Towards Provable Minimax Equilibrium via Multi-Generator Architectures

A Constituent-Centric Neural Architecture for Reading Comprehension.

Fault Tolerance in Iterative-Convergent Machine Learning