In this paper, we propose the new Ball Ranking Machines (BRMs) to address the supervised ranking problems. In previous work, supervised ranking methods have been successfully applied in various information retrieval tasks. Among these methodologies, the Ranking Support Vector Machines (Rank SVMs) are well investigated. However, one major fact limiting their applications is that Ranking SVMs need optimize a margin-based objective function over all possible document pairs within all queries on the training set. In consequence, Ranking SVMs need select a large number of support vectors among a huge number of support vector candidates. This paper introduces a new model of of Ranking SVMs and develops an efficient approximation algorithm, which decreases the training time and generates much fewer support vectors. Empirical studies on synthetic data and content-based image/video retrieval data show that our method is comparable to Ranking SVMs in accuracy, but use much fewer ranking support vectors and significantly less training time.

We propose a new clustering based low-rank matrix approximation method, Cluster Indicator Decomposition (CID), which yields more accurate low-rank approximations than previous commonly used singular value decomposition and other Nyström style decompositions. Our model utilizes the intrinsic structures of data and theoretically be more compact and accurate than the traditional low rank approximation approaches. The reconstruction in CID is extremely fast leading to a desirable advantage of our method in large-scale kernel machines (like Support Vector Machines) in which the reconstruction of the kernels needs to be frequently computed. Experimental results indicate that our approach compress images much more efficiently than other factorization based methods. We show that combining our method with Support Vector Machines obtains more accurate approximation and more accurate prediction while consuming much less computation resources.

In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at least $1-\rho$ in at most $O(\tfrac{n}{\epsilon} \log \tfrac{1}{\rho})$ iterations, where $n$ is the number of blocks. For strongly convex functions the method converges linearly. This extends recent results of Nesterov [Efficiency of coordinate descent methods on huge-scale optimization problems, CORE Discussion Paper #2010/2], which cover the smooth case, to composite minimization, while at the same time improving the complexity by the factor of 4 and removing $\epsilon$ from the logarithmic term. More importantly, in contrast with the aforementioned work in which the author achieves the results by applying the method to a regularized version of the objective function with an unknown scaling factor, we show that this is not necessary, thus achieving true iteration complexity bounds. In the smooth case we also allow for arbitrary probability vectors and non-Euclidean norms. Finally, we demonstrate numerically that the algorithm is able to solve huge-scale $\ell_1$-regularized least squares and support vector machine problems with a billion variables.

We study the relationship between content and temporal dynamics of information on Twitter, focusing on the persistence of information. We compare two extreme temporal patterns in the decay rate of URLs embedded in tweets, defining a prediction task to distinguish between URLs that fade rapidly following their peak of popularity and those that fade more slowly. Our experiments show a strong association between the content and the temporal dynamics of information: given unigram features extracted from corresponding HTML webpages, a linear SVM classifier can predict the temporal pattern of URLs with high accuracy. We further explore the content of URLs in the two temporal classes using various textual analysis techniques (via LIWC and trend detection). We find that the rapidly-fading information contains significantly more words related to negative emotion, actions, and more complicated cognitive processes, whereas the persistent information contains more words related to positive emotion, leisure, and lifestyle.

Estimation of a person's influence and personality traits from social media data has many applications. We use social linkage criteria, such as number of followers and friends, as proxies to form corpora, from popular blogging site Livejournal, for examining two two-class classification problems: influential vs. non-influential, and extraversion vs. introversion. Classification is performed using automatically-derived psycholinguistic and mood-based features of a user's textual messages. We experiment with three sub-corpora of 10000 users each, and present the most effective predictors for each category. The best classification result, at 80%, is achieved using psycholinguistic features; e.g., influentials are found to use more complex language, than non-influentials, and use more leisure-related terms.

We describe a novel binary classification technique called Banded SVM (B-SVM). In the standard C-SVM formulation of Cortes et al. (1995), the decision rule is encouraged to lie in the interval [1, \infty]. The new B-SVM objective function contains a penalty term that encourages the decision rule to lie in a user specified range [\rho_1, \rho_2]. In addition to the standard set of support vectors (SVs) near the class boundaries, B-SVM results in a second set of SVs in the interior of each class.

Machine learning is an established method of selecting algorithms to solve hard search problems. Despite this, to date no systematic comparison and evaluation of the different techniques has been performed and the performance of existing systems has not been critically compared to other approaches. We compare machine learning techniques for algorithm selection on real-world data sets of hard search problems. In addition to well-established approaches, for the first time we also apply statistical relational learning to this problem. We demonstrate that most machine learning techniques and existing systems perform less well than one might expect. To guide practitioners, we close by giving clear recommendations as to which machine learning techniques are likely to perform well based on our experiments.

Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are given to the learner prior to learning. Although transduction seems at the outset to be an easier task than induction, there have not been many provably useful algorithms for transduction. Moreover, the precise relation between induction and transduction has not yet been determined. The main theoretical developments related to transduction were presented by Vapnik more than twenty years ago. One of Vapnik's basic results is a rather tight error bound for transductive classification based on an exact computation of the hypergeometric tail. While tight, this bound is given implicitly via a computational routine. Our first contribution is a somewhat looser but explicit characterization of a slightly extended PAC-Bayesian version of Vapnik's transductive bound. This characterization is obtained using concentration inequalities for the tail of sums of random variables obtained by sampling without replacement. We then derive error bounds for compression schemes such as (transductive) support vector machines and for transduction algorithms based on clustering. The main observation used for deriving these new error bounds and algorithms is that the unlabeled test points, which in the transductive setting are known in advance, can be used in order to construct useful data dependent prior distributions over the hypothesis space.

Motivation: Biomarker discovery from high-dimensional data is a crucial problem with enormous applications in biology and medicine. It is also extremely challenging from a statistical viewpoint, but surprisingly few studies have investigated the relative strengths and weaknesses of the plethora of existing feature selection methods. Methods: We compare 32 feature selection methods on 4 public gene expression datasets for breast cancer prognosis, in terms of predictive performance, stability and functional interpretability of the signatures they produce. Results: We observe that the feature selection method has a significant influence on the accuracy, stability and interpretability of signatures. Simple filter methods generally outperform more complex embedded or wrapper methods, and ensemble feature selection has generally no positive effect. Overall a simple Student's t-test seems to provide the best results. Availability: Code and data are publicly available at http://cbio.ensmp.fr/~ahaury/.

In this paper, we propose to (seamlessly) integrate b-bit minwise hashing with linear SVM to substantially improve the training (and testing) efficiency using much smaller memory, with essentially no loss of accuracy. Theoretically, we prove that the resemblance matrix, the minwise hashing matrix, and the b-bit minwise hashing matrix are all positive definite matrices (kernels). Interestingly, our proof for the positive definiteness of the b-bit minwise hashing kernel naturally suggests a simple strategy to integrate b-bit hashing with linear SVM. Our technique is particularly useful when the data can not fit in memory, which is an increasingly critical issue in large-scale machine learning. Our preliminary experimental results on a publicly available webspam dataset (350K samples and 16 million dimensions) verified the effectiveness of our algorithm. For example, the training time was reduced to merely a few seconds. In addition, our technique can be easily extended to many other linear and nonlinear machine learning applications such as logistic regression.