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Proceedings Article

Learning Rankings via Convex Hull Separation

05 Dec 2005-Vol. 18, pp 395-402
TL;DR: Experiments indicate that the proposed algorithm for learning ranking functions from order constraints between sets—i.e. classes—of training samples is at least as accurate as the current state-of-the-art and several orders of magnitude faster than current methods.
Abstract: We propose efficient algorithms for learning ranking functions from order constraints between sets—i.e. classes—of training samples. Our algorithms may be used for maximizing the generalized Wilcoxon Mann Whitney statistic that accounts for the partial ordering of the classes: special cases include maximizing the area under the ROC curve for binary classification and its generalization for ordinal regression. Experiments on public benchmarks indicate that: (a) the proposed algorithm is at least as accurate as the current state-of-the-art; (b) computationally, it is several orders of magnitude faster and—unlike current methods—it is easily able to handle even large datasets with over 20,000 samples.

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Citations
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Journal ArticleDOI
TL;DR: The proposed framework to adaptively learn transferable representations called super-features from the training data of both the target task and the auxiliary task is sufficiently flexible to deal with complicated common structures among different learning tasks.
Abstract: In learning to rank, both the quality and quantity of the training data have significant impacts on the performance of the learned ranking functions. However, in many applications, there are usually not sufficient labeled training data for the construction of an accurate ranking model. It is therefore desirable to leverage existing training data from other tasks when learning the ranking function for a particular task, an important problem which we tackle in this article utilizing a boosting framework with transfer learning. In particular, we propose to adaptively learn transferable representations called super-features from the training data of both the target task and the auxiliary task. Those super-features and the coefficients for combining them are learned in an iterative stage-wise fashion. Unlike previous transfer learning methods, the super-features can be adaptively learned by weak learners from the data. Therefore, the proposed framework is sufficiently flexible to deal with complicated common structures among different learning tasks. We evaluate the performance of the proposed transfer learning method for two datasets from the Letor collection and one dataset collected from a commercial search engine, and we also compare our methods with several existing transfer learning methods. Our results demonstrate that the proposed method can enhance the ranking functions of the target tasks utilizing the training data from the auxiliary tasks.

2 citations

02 Nov 2011
TL;DR: This paper shows that the hard margin case is approximately reduced to a soft margin optimization problem over p + n instances for which the resulting linear classifier is guaranteed to have a certain margin over pairs.
Abstract: Finding linear classifiers that maximize AUC scores is important in ranking research. This is naturally formulated as a 1-norm hard/soft margin optimization problem over pn pairs of p positive and n negative instances. However, directly solving the optimization problems is impractical since the problem size (pn) is quadratically larger than the given sample size (p + n). In this paper, we give (approximate) reductions from the problems to hard/soft margin optimization problems of linear size. First, for the hard margin case, we show that the problem is reduced to a hard margin optimization problem over p + n instances in which the bias constant term is to be optimized. Then, for the soft margin case, we show that the problem is approximately reduced to a soft margin optimization problem over p + n instances for which the resulting linear classifier is guaranteed to have a certain margin over pairs.

1 citations


Cites methods from "Learning Rankings via Convex Hull S..."

  • ...[10] proposed reduction methods from RankSVMs or 2-norm soft margin optimization over pairs to 2-norm soft margin optimization over instances....

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Proceedings Article
01 Jan 2007
TL;DR: The main thesis of this paper is that the design of task-specific learning machines is aided substantially by using a convex optimization solver as a back-end to implement the task, liberating the designer from the concern of designing and analyzing an ad hoc algorithm.
Abstract: This paper reviews the recent surge of interest in convex optimization in a context of pattern recognition and machine learning. The main thesis of this paper is that the design of task-specific learning machines is aided substantially by using a convex optimization solver as a back-end to implement the task, liberating the designer from the concern of designing and analyzing an ad hoc algorithm. The aim of this paper is twofold: (i) it phrases the contributions of this ESANN 2007 special session in a broader context, and (ii) it provides a road-map to published results in this context.

1 citations


Cites methods from "Learning Rankings via Convex Hull S..."

  • ...This task were cast in the framework of SVMs as in [31, 17, 25]....

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Proceedings ArticleDOI
03 Mar 2013
TL;DR: A completely automatic facial expression recognition system is presented in this paper, which consists of three main procedures based on skin color blocks and geometrical properties applied to eliminate the skin color regions that do not belong to the face in the HSV color space.
Abstract: A completely automatic facial expression recognition system is presented in this paper, which consists of three main procedures. The first is based on skin color blocks and geometrical properties applied to eliminate the skin color regions that do not belong to the face in the HSV color space. Than we find proper ranges of eyes, mouth, and eyebrows according to the positions of pupils and center of a mouth. Subsequently, we perform both the edge detection and binarization operations on the above ranged images to obtain 16 landmarks. After manipulating these landmarks, 16 characteristic distances are the facial feature produced to represent a kind of expressions. Finally, we subtract the 16 characteristic distances of a neutral face from the 16 characteristic distances of a certain expression to acquire its 16 displacement values fed to a classifier with an incremental learning scheme, which can identify six kinds of expressions: joy, anger, surprise, fear, sadness, and neutral. We choose the AdaRank model as the core technique to implement our strong facial expression classifier. Our model, referred to as AdaRank, repeatedly constructs classifiers on the basis of re-weighted training data and finally linearly combines the classifiers for making ranking predictions. Through conducting many experiments, the statistics of performance reveals that the accuracy rate of our facial expression recognition system reaches more than 95%.

1 citations

Patent
02 Jan 2020
TL;DR: In this paper, the authors present systems, methods, and non-transitory computer readable media that utilize a genetic framework to generate enhanced digital layouts from digital content fragments, which can efficiently utilize computing resources to generate a digital layout from a layout chromosome that is optimized to specified platforms, distribution audiences and target optimization goals.
Abstract: The present disclosure includes systems, methods, and non-transitory computer readable media that utilize a genetic framework to generate enhanced digital layouts from digital content fragments. In particular, in one or more embodiments, the disclosed systems iteratively generate a layout chromosome of digital content fragments, determine a fitness level of the layout chromosome, and mutate the layout chromosome until converging to an improved fitness level. The disclosed systems can efficiently utilize computing resources to generate a digital layout from a layout chromosome that is optimized to specified platforms, distribution audiences, and target optimization goals.
References
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Book
Vladimir Vapnik1
01 Jan 1995
TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
Abstract: Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing learning algorithms what is important in learning theory?.

40,147 citations


"Learning Rankings via Convex Hull S..." refers background in this paper

  • ...Note that enforcing the constraints defined above indeed implies the desired ordering, since we have: Aw + y ≥ −γ ≥ γ̂ + 1 ≥ γ̂ ≥ Aw − y It is also important to note the connection with Support Vector Machines (SVM) formulation [10, 14] for the binary case....

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Book
01 Jan 1983
TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
Abstract: The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components).

23,215 citations


"Learning Rankings via Convex Hull S..." refers methods in this paper

  • ...Ordinal regression and methods for handling structured output classes: For a classic description of generalized linear models for ordinal regre ssion, see [11]....

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01 Feb 1977

5,933 citations


"Learning Rankings via Convex Hull S..." refers background in this paper

  • ...B′u− w′[A− ′ − A+ ′ ] = 0, b′u ≤ −1, u ≥ 0, (7) Where the second equivalent form of the constraints was obtained by negation (as before), and the third equivalent form results from ourthird key insight: the application of Farka’s theorem of alternatives[9]....

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Proceedings ArticleDOI
23 Jul 2002
TL;DR: The goal of this paper is to develop a method that utilizes clickthrough data for training, namely the query-log of the search engine in connection with the log of links the users clicked on in the presented ranking.
Abstract: This paper presents an approach to automatically optimizing the retrieval quality of search engines using clickthrough data. Intuitively, a good information retrieval system should present relevant documents high in the ranking, with less relevant documents following below. While previous approaches to learning retrieval functions from examples exist, they typically require training data generated from relevance judgments by experts. This makes them difficult and expensive to apply. The goal of this paper is to develop a method that utilizes clickthrough data for training, namely the query-log of the search engine in connection with the log of links the users clicked on in the presented ranking. Such clickthrough data is available in abundance and can be recorded at very low cost. Taking a Support Vector Machine (SVM) approach, this paper presents a method for learning retrieval functions. From a theoretical perspective, this method is shown to be well-founded in a risk minimization framework. Furthermore, it is shown to be feasible even for large sets of queries and features. The theoretical results are verified in a controlled experiment. It shows that the method can effectively adapt the retrieval function of a meta-search engine to a particular group of users, outperforming Google in terms of retrieval quality after only a couple of hundred training examples.

4,453 citations

Book
01 Jan 1969
TL;DR: It is shown that if A is closed for all k → x x, k → y y, where ( k A ∈ ) k y x , then ( ) A ∉ y x .
Abstract: Part 1 (if): Assume that Z is closed. We must show that if A is closed for all k → x x , k → y y , where ( k A ∈ ) k y x , then ( ) A ∈ y x . By the definition of Z being closed, we know that all points arbitrarily close to Z are in Z. Let k → x x , k → y y , and ( k A ∈ ) k y x . Now, for any ε > 0, there exists an N such that for all k ≥ N we have || || k ε − < x x , || || k ε − < y y which implies that ( ) , x y is arbitrarily close to Z, so ( ) , x y ∈ Z and ( ) A ∈ y x . Thus, A is closed.

2,146 citations


"Learning Rankings via Convex Hull S..." refers background in this paper

  • ...Bu− w[A ′ − A ′ ] = 0, bu ≤ −1, u ≥ 0, (7) Where the second equivalent form of the constraints was obtai ned by negation (as before), and the third equivalent form results from our third key insight: the application of Farka’s theorem of alternatives[9]....

    [...]