8,286 research outputs found
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
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
Optimizing Ranking Measures for Compact Binary Code Learning
Hashing has proven a valuable tool for large-scale information retrieval.
Despite much success, existing hashing methods optimize over simple objectives
such as the reconstruction error or graph Laplacian related loss functions,
instead of the performance evaluation criteria of interest---multivariate
performance measures such as the AUC and NDCG. Here we present a general
framework (termed StructHash) that allows one to directly optimize multivariate
performance measures. The resulting optimization problem can involve
exponentially or infinitely many variables and constraints, which is more
challenging than standard structured output learning. To solve the StructHash
optimization problem, we use a combination of column generation and
cutting-plane techniques. We demonstrate the generality of StructHash by
applying it to ranking prediction and image retrieval, and show that it
outperforms a few state-of-the-art hashing methods.Comment: Appearing in Proc. European Conference on Computer Vision 201
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 â„“p-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
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