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

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

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Data Mining - Concepts and Techniques.

Reducing the web latency is one of the primary concerns of Internet research. Web caching and web prefetching are two effective techniques to latency reduction. A primary method for intelligent prefetching is to rank potential web documents based on prediction models that are trained on the past web server and proxy server log data, and to prefetch the highly ranked objects. For this method to work well, the prediction model must be updated constantly, and different queries must be answered efficiently. In this paper we present a data-cube model to represent Web access sessions for data mining for supporting the prediction model construction. The cube model organizes session data into three dimensions. With the data cube in place, we apply efficient data mining algorithms for clustering and correlation analysis. As a result of the analysis, the web page clusters can then be used to guide the prefetching system. In this paper, we propose an integrated web-caching and web-prefetching model, where the issues of prefetching aggressiveness, replacement policy and increased network traffic are addressed together in an integrated framework. The core of our integrated solution is a prediction model based on statistical correlation between web objects. This model can be frequently updated by querying the data cube of web server logs. This integrated data cube and prediction based prefetching framework represents a first such effort in our knowledge.

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A data cube model for prediction-based web prefetching

Heterogeneous transfer learning has recently gained much attention as a new machine learning paradigm in which the knowledge can be transferred from source domains to target domains in different feature spaces. Existing works usually assume that source domains can provide accurate and useful knowledge to be transferred to target domains for learning. In practice, there may be noise appearing in given source (text) and target (image) domains data, and thus, the performance of transfer learning can be seriously degraded. In this paper, we propose a robust and non-negative collective matrix factorization model to handle noise in text-to-image transfer learning, and make a reliable bridge to transfer accurate and useful knowledge from the text domain to the image domain. The proposed matrix factorization model can be solved by an efficient iterative method, and the convergence of the iterative method can be shown. Extensive experiments on real data sets suggest that the proposed model is able to effectively perform transfer learning in noisy text and image domains, and it is superior to the popular existing methods for text-to-image transfer learning.

Robust and Non-Negative Collective Matrix Factorization for Text-to-Image Transfer Learning

Color image restoration is one of the important tasks in color image processing. Total variation regularizaton was proposed and employed for the recovery of edges in a grayscale image. In the liter...

Color image restoration by saturation-value total variation

We consider the system of linear equations Lu=f, where L is a nonsymmetric block Toeplitz-like-plus-diagonal matrix, which arises from the Sinc-Galerkin discretization of differential equations. Our main contribution is to construct effective preconditioners for this structured coefficient matrix and to derive tight bounds for eigenvalues of the preconditioned matrices. Moreover, we use numerical examples to show that the new preconditioners, when applied to the preconditioned GMRES method, are efficient for solving the system of linear equations.

Preconditioners for nonsymmetric block toeplitz-like-plus-diagonal linear systems

Since the early 1980s, the concept of relationship marketing has been becoming important in general marketing, especially in the area of direct and interactive marketing. The core of relationship marketing is the maintenance of long-term relationships with the customers. However, the relationship marketing is costly and therefore, the determination of the customer lifetime value (CLV) is an important element in making strategic decisions in both advertising and promotion. In this paper, we propose a stochastic dynamic programming model with a Markov chain for the optimization of CLV. Both cases of infinite horizon and finite horizon are discussed. The model is then applied to practical data of a computer service company.

https://link.springer.com/content/pdf/10.1057%2Fpalgrave.jors.2601755.pdf

Michael K. Ng

Papers

A data cube model for prediction-based web prefetching

Robust and Non-Negative Collective Matrix Factorization for Text-to-Image Transfer Learning

Color image restoration by saturation-value total variation

Preconditioners for nonsymmetric block toeplitz-like-plus-diagonal linear systems

Customer lifetime value: Stochastic optimization approach