Pairwise learning usually refers to a learning task which involves a loss function depending on pairs of examples, among which most notable ones include ranking, metric learning and AUC maximization. In this paper, we study an online algorithm for pairwise learning with a least-square loss function in an unconstrained setting of a reproducing kernel Hilbert space (RKHS), which we refer to as the Online Pairwise lEaRning Algorithm (OPERA). In contrast to existing works \cite{Kar,Wang} which require that the iterates are restricted to a bounded domain or the loss function is strongly-convex, OPERA is associated with a non-strongly convex objective function and learns the target function in an unconstrained RKHS. Specifically, we establish a general theorem which guarantees the almost surely convergence for the last iterate of OPERA without any assumptions on the underlying distribution. Explicit convergence rates are derived under the condition of polynomially decaying step sizes. We also establish an interesting property for a family of widely-used kernels in the setting of pairwise learning and illustrate the above convergence results using such kernels. Our methodology mainly depends on the characterization of RKHSs using its associated integral operators and probability inequalities for random variables with values in a Hilbert space.

We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing approximate inference techniques such as belief propagation, mean field, and variants. We show that a recently proposed variational approach to inference in log-supermodular models -L-FIELD- reduces to the widely-studied minimum norm problem for submodular minimization. This insight allows to leverage powerful existing tools, and hence to solve the variational problem orders of magnitude more efficiently than previously possible. We then provide another natural interpretation of L-FIELD, demonstrating that it exactly minimizes a specific type of R\'enyi divergence measure. This insight sheds light on the nature of the variational approximations produced by L-FIELD. Furthermore, we show how to perform parallel inference as message passing in a suitable factor graph at a linear convergence rate, without having to sum up over all the configurations of the factor. Finally, we apply our approach to a challenging image segmentation task. Our experiments confirm scalability of our approach, high quality of the marginals, and the benefit of incorporating higher-order potentials.

This paper deals with the binary classification task when the target class has the lower probability of occurrence. In such situation, it is not possible to build a powerful classifier by using standard methods such as logistic regression, classification tree, discriminant analysis, etc. To overcome this short-coming of these methods which yield classifiers with low sensibility, we tackled the classification problem here through an approach based on the association rules learning. This approach has the advantage of allowing the identification of the patterns that are well correlated with the target class. Association rules learning is a well known method in the area of data-mining. It is used when dealing with large database for unsupervised discovery of local patterns that expresses hidden relationships between input variables. In considering association rules from a supervised learning point of view, a relevant set of weak classifiers is obtained from which one derives a classifier that performs well.

Dempster-Shafer evidence theory is an efficient mathematical tool to deal with uncertain information. In that theory, basic probability assignment (BPA) is the basic element for the expression and inference of uncertainty. Decision-making based on BPA is still an open issue in Dempster-Shafer evidence theory. In this paper, a novel approach of transforming basic probability assignments to probabilities is proposed based on Deng entropy which is a new measure for the uncertainty of BPA. The principle of the proposed method is to minimize the difference of uncertainties involving in the given BPA and obtained probability distribution. Numerical examples are given to show the proposed approach.

This paper uses natural language processing to create the first machine-coded democracy index, which I call Automated Democracy Scores (ADS). The ADS are based on 42 million news articles from 6,043 different sources and cover all independent countries in the 1993-2012 period. Unlike the democracy indices we have today the ADS are replicable and have standard errors small enough to actually distinguish between cases. The ADS are produced with supervised learning. Three approaches are tried: a) a combination of Latent Semantic Analysis and tree-based regression methods; b) a combination of Latent Dirichlet Allocation and tree-based regression methods; and c) the Wordscores algorithm. The Wordscores algorithm outperforms the alternatives, so it is the one on which the ADS are based. There is a web application where anyone can change the training set and see how the results change: democracy-scores.org

MILJS is a collection of state-of-the-art, platform-independent, scalable, fast JavaScript libraries for matrix calculation and machine learning. Our core library offering a matrix calculation is called Sushi, which exhibits far better performance than any other leading machine learning libraries written in JavaScript. Especially, our matrix multiplication is 177 times faster than the fastest JavaScript benchmark. Based on Sushi, a machine learning library called Tempura is provided, which supports various algorithms widely used in machine learning research. We also provide Soba as a visualization library. The implementations of our libraries are clearly written, properly documented and thus can are easy to get started with, as long as there is a web browser. These libraries are available from http://mil-tokyo.github.io/

We seek decision rules for prediction-time cost reduction, where complete data is available for training, but during prediction-time, each feature can only be acquired for an additional cost. We propose a novel random forest algorithm to minimize prediction error for a user-specified {\it average} feature acquisition budget. While random forests yield strong generalization performance, they do not explicitly account for feature costs and furthermore require low correlation among trees, which amplifies costs. Our random forest grows trees with low acquisition cost and high strength based on greedy minimax cost-weighted-impurity splits. Theoretically, we establish near-optimal acquisition cost guarantees for our algorithm. Empirically, on a number of benchmark datasets we demonstrate superior accuracy-cost curves against state-of-the-art prediction-time algorithms.

As one of the most important types of (weaker) supervised information in machine learning and pattern recognition, pairwise constraint, which specifies whether a pair of data points occur together, has recently received significant attention, especially the problem of pairwise constraint propagation. At least two reasons account for this trend: the first is that compared to the data label, pairwise constraints are more general and easily to collect, and the second is that since the available pairwise constraints are usually limited, the constraint propagation problem is thus important. This paper provides an up-to-date critical survey of pairwise constraint propagation research. There are two underlying motivations for us to write this survey paper: the first is to provide an up-to-date review of the existing literature, and the second is to offer some insights into the studies of pairwise constraint propagation. To provide a comprehensive survey, we not only categorize existing propagation techniques but also present detailed descriptions of representative methods within each category.

In our previous works, we proposed a physically-inspired rule to organize the data points into an in-tree (IT) structure, in which some undesired edges are allowed to occur. By removing those undesired or redundant edges, this IT structure is divided into several separate parts, each representing one cluster. In this work, we seek to prevent the undesired edges from arising at the source. Before using the physically-inspired rule, data points are at first organized into a proximity graph which restricts each point to select the optimal directed neighbor just among its neighbors. Consequently, separated in-trees or clusters automatically arise, without redundant edges requiring to be removed.

Non-orthogonal joint diagonalization (NJD) free of prewhitening has been widely studied in the context of blind source separation (BSS) and array signal processing, etc. However, NJD is used to retrieve the jointly diagonalizable structure for a single set of target matrices which are mostly formulized with a single dataset, and thus is insufficient to handle multiple datasets with inter-set dependences, a scenario often encountered in joint BSS (J-BSS) applications. As such, we present a generalized NJD (GNJD) algorithm to simultaneously perform asymmetric NJD upon multiple sets of target matrices with mutually linked loading matrices, by using LU decomposition and successive rotations, to enable J-BSS over multiple datasets with indication/exploitation of their mutual dependences. Experiments with synthetic and real-world datasets are provided to illustrate the performance of the proposed algorithm.