Margin-based Ranking and an Equivalence between AdaBoost and RankBoost

We study boosting algorithms for learning to rank. We give a general margin-based bound for ranking based on covering numbers for the hypothesis space. Our bound suggests that algorithms that maximize the ranking margin will generalize well. We then describe a new algorithm, smooth margin ranking, that precisely converges to a maximum ranking-margin solution. The algorithm is a modification of RankBoost, analogous to “approximate coordinate ascent boosting.” Finally, we prove that AdaBoost and RankBoost are equally good for the problems of bipartite ranking and classification in terms of their asymptotic behavior on the training set. Under natural conditions, AdaBoost achieves an area under the ROC curve that is equally as good as RankBoost’s; furthermore, RankBoost, when given a specific intercept, achieves a misclassification error that is as good as AdaBoost’s. This may help to explain the empirical observations made by Cortes andMohri, and Caruana and Niculescu-Mizil, about the excellent performance of AdaBoost as a bipartite ranking algorithm, as measured by the area under the ROC curve

The P-Norm Push: A Simple Convex Ranking Algorithm that Concentrates at the Top of the List

We are interested in supervised ranking algorithms that perform especially well near the top of the ranked list, and are only required to perform sufficiently well on the rest of the list. In this work, we provide a general form of convex objective that gives high-scoring examples more importance. This “push” near the top of the list can be chosen arbitrarily large or small, based on the preference of the user. We choose ℓp-norms to provide a specific type of push; if the user sets p larger, the objective concentrates harder on the top of the list. We derive a generalization bound based on the p-norm objective, working around the natural asymmetry of the problem. We then derive a boosting-style algorithm for the problem of ranking with a push at the top. The usefulness of the algorithm is illustrated through experiments on repository data. We prove that the minimizer of the algorithm’s objective is unique in a specific sense. Furthermore, we illustrate how our objective is related to quality measurements for information retrieval

RandomBoost: Simplified Multi-class Boosting through Randomization

We propose a novel boosting approach to multi-class classification problems, in which multiple classes are distinguished by a set of random projection matrices in essence. The approach uses random projections to alleviate the proliferation of binary classifiers typically required to perform multi-class classification. The result is a multi-class classifier with a single vector-valued parameter, irrespective of the number of classes involved. Two variants of this approach are proposed. The first method randomly projects the original data into new spaces, while the second method randomly projects the outputs of learned weak classifiers. These methods are not only conceptually simple but also effective and easy to implement. A series of experiments on synthetic, machine learning and visual recognition data sets demonstrate that our proposed methods compare favorably to existing multi-class boosting algorithms in terms of both the convergence rate and classification accuracy.Comment: 15 page

Active Sampling of Pairs and Points for Large-scale Linear Bipartite Ranking

Bipartite ranking is a fundamental ranking problem that learns to order relevant instances ahead of irrelevant ones. The pair-wise approach for bi-partite ranking construct a quadratic number of pairs to solve the problem, which is infeasible for large-scale data sets. The point-wise approach, albeit more efficient, often results in inferior performance. That is, it is difficult to conduct bipartite ranking accurately and efficiently at the same time. In this paper, we develop a novel active sampling scheme within the pair-wise approach to conduct bipartite ranking efficiently. The scheme is inspired from active learning and can reach a competitive ranking performance while focusing only on a small subset of the many pairs during training. Moreover, we propose a general Combined Ranking and Classification (CRC) framework to accurately conduct bipartite ranking. The framework unifies point-wise and pair-wise approaches and is simply based on the idea of treating each instance point as a pseudo-pair. Experiments on 14 real-word large-scale data sets demonstrate that the proposed algorithm of Active Sampling within CRC, when coupled with a linear Support Vector Machine, usually outperforms state-of-the-art point-wise and pair-wise ranking approaches in terms of both accuracy and efficiency.Comment: a shorter version was presented in ACML 201

An efficient boosting algorithm for combining preferences

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (p. 79-84).by Raj Dharmarajan Iyer, Jr.S.M

From Ordinal Ranking to Binary Classification

We study the ordinal ranking problem in machine learning. The problem can be viewed as a classification problem with additional ordinal information or as a regression problem without actual numerical information. From the classification perspective, we formalize the concept of ordinal information by a cost-sensitive setup, and propose some novel cost-sensitive classification algorithms. The algorithms are derived from a systematic cost-transformation technique, which carries a strong theoretical guarantee. Experimental results show that the novel algorithms perform well both in a general cost-sensitive setup and in the specific ordinal ranking setup. From the regression perspective, we propose the threshold ensemble model for ordinal ranking, which allows the machines to estimate a real-valued score (like regression) before quantizing it to an ordinal rank. We study the generalization ability of threshold ensembles and derive novel large-margin bounds on its expected test performance. In addition, we improve an existing algorithm and propose a novel algorithm for constructing large-margin threshold ensembles. Our proposed algorithms are efficient in training and achieve decent out-of-sample performance when compared with the state-of-the-art algorithm on benchmark data sets. We then study how ordinal ranking can be reduced to weighted binary classification. The reduction framework is simpler than the cost-sensitive classification approach and includes the threshold ensemble model as a special case. The framework allows us to derive strong theoretical results that tightly connect ordinal ranking with binary classification. We demonstrate the algorithmic and theoretical use of the reduction framework by extending SVM and AdaBoost, two of the most popular binary classification algorithms, to the area of ordinal ranking. Coupling SVM with the reduction framework results in a novel and faster algorithm for ordinal ranking with superior performance on real-world data sets, as well as a new bound on the expected test performance for generalized linear ordinal rankers. Coupling AdaBoost with the reduction framework leads to a novel algorithm that boosts the training accuracy of any cost-sensitive ordinal ranking algorithms theoretically, and in turn improves their test performance empirically. From the studies above, the key to improve ordinal ranking is to improve binary classification. In the final part of the thesis, we include two projects that aim at understanding binary classification better in the context of ensemble learning. First, we discuss how AdaBoost is restricted to combining only a finite number of hypotheses and remove the restriction by formulating a framework of infinite ensemble learning based on SVM. The framework can output an infinite ensemble through embedding infinitely many hypotheses into an~SVM kernel. Using the framework, we show that binary classification (and hence ordinal ranking) can be improved by going from a finite ensemble to an infinite one. Second, we discuss how AdaBoost carries the property of being resistant to overfitting. Then, we propose the SeedBoost algorithm, which uses the property as a machinery to prevent other learning algorithms from overfitting. Empirical results demonstrate that SeedBoost can indeed improve an overfitting algorithm on some data sets.</p

SemRank: ranking refinement strategy by using the semantic intensity

AbstractThe ubiquity of the multimedia has raised a need for the system that can store, manage, structured the multimedia data in such a way that it can be retrieved intelligently. One of the current issues in media management or data mining research is ranking of retrieved documents. Ranking is one of the provocative problems for information retrieval systems. Given a user query comes up with the millions of relevant results but if the ranking function cannot rank it according to the relevancy than all results are just obsolete. However, the current ranking techniques are in the level of keyword matching. The ranking among the results is usually done by using the term frequency. This paper is concerned with ranking the document relying merely on the rich semantic inside the document instead of the contents. Our proposed ranking refinement strategy known as SemRank, rank the document based on the semantic intensity. Our approach has been applied on the open benchmark LabelMe dataset and compared against one of the well known ranking model i.e. Vector Space Model (VSM). The experimental results depicts that our approach has achieved significant improvement in retrieval performance over the state of the art ranking methods

Generalized Boosting Algorithms for Convex Optimization

Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting with respect to any convex objective and introduce a new measure of weak learner performance into this setting which generalizes existing work. We present the weak to strong learning guarantees for the existing gradient boosting work for strongly-smooth, strongly-convex objectives under this new measure of performance, and also demonstrate that this work fails for non-smooth objectives. To address this issue, we present new algorithms which extend this boosting approach to arbitrary convex loss functions and give corresponding weak to strong convergence results. In addition, we demonstrate experimental results that support our analysis and demonstrate the need for the new algorithms we present.Comment: Extended version of paper presented at the International Conference on Machine Learning, 2011. 9 pages + appendix with proof