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193
Covariate shift adaptation by importance weighted cross validation
, 2000
"... A common assumption in supervised learning is that the input points in the training set follow the same probability distribution as the input points that will be given in the future test phase. However, this assumption is not satisfied, for example, when the outside of the training region is extrapo ..."
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Cited by 122 (55 self)
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A common assumption in supervised learning is that the input points in the training set follow the same probability distribution as the input points that will be given in the future test phase. However, this assumption is not satisfied, for example, when the outside of the training region is extrapolated. The situation where the training input points and test input points follow different distributions while the conditional distribution of output values given input points is unchanged is called the covariate shift. Under the covariate shift, standard model selection techniques such as cross validation do not work as desired since its unbiasedness is no longer maintained. In this paper, we propose a new method called importance weighted cross validation (IWCV), for which we prove its unbiasedness even under the covariate shift. The IWCV procedure is the only one that can be applied for unbiased classification under covariate shift, whereas alternatives to IWCV exist for regression. The usefulness of our proposed method is illustrated by simulations, and furthermore demonstrated in the braincomputer interface, where strong nonstationarity effects can be seen between training and test sessions. c2000 Masashi Sugiyama, Matthias Krauledat, and KlausRobert Müller.
Protovalue functions: A laplacian framework for learning representation and control in markov decision processes
 Journal of Machine Learning Research
, 2006
"... This paper introduces a novel spectral framework for solving Markov decision processes (MDPs) by jointly learning representations and optimal policies. The major components of the framework described in this paper include: (i) A general scheme for constructing representations or basis functions by d ..."
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Cited by 92 (10 self)
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This paper introduces a novel spectral framework for solving Markov decision processes (MDPs) by jointly learning representations and optimal policies. The major components of the framework described in this paper include: (i) A general scheme for constructing representations or basis functions by diagonalizing symmetric diffusion operators (ii) A specific instantiation of this approach where global basis functions called protovalue functions (PVFs) are formed using the eigenvectors of the graph Laplacian on an undirected graph formed from state transitions induced by the MDP (iii) A threephased procedure called representation policy iteration comprising of a sample collection phase, a representation learning phase that constructs basis functions from samples, and a final parameter estimation phase that determines an (approximately) optimal policy within the (linear) subspace spanned by the (current) basis functions. (iv) A specific instantiation of the RPI framework using leastsquares policy iteration (LSPI) as the parameter estimation method (v) Several strategies for scaling the proposed approach to large discrete and continuous state spaces, including the Nyström extension for outofsample interpolation of eigenfunctions, and the use of Kronecker sum factorization to construct compact eigenfunctions in product spaces such as factored MDPs (vi) Finally, a series of illustrative discrete and continuous control tasks, which both illustrate the concepts and provide a benchmark for evaluating the proposed approach. Many challenges remain to be addressed in scaling the proposed framework to large MDPs, and several elaboration of the proposed framework are briefly summarized at the end.
Semisupervised graphbased hyperspectral image classification
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2007
"... This paper presents a semisupervised graphbased method for the classification of hyperspectral images. The method is designed to handle the special characteristics of hyperspectral images, namely high input dimension of pixels, low number of labeled samples, and spatial variability of the spectral ..."
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Cited by 50 (6 self)
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This paper presents a semisupervised graphbased method for the classification of hyperspectral images. The method is designed to handle the special characteristics of hyperspectral images, namely high input dimension of pixels, low number of labeled samples, and spatial variability of the spectral signature. To alleviate these problems, the method incorporates three ingredients, respectively. First, being a kernelbased method, it combats the curse of dimensionality efficiently. Second, following a semisupervised approach, it exploits the wealth of unlabeled samples in the image, and naturally gives relative importance to the labeled ones through a graphbased methodology. Finally, it incorporates contextual information through a full family of composite kernels. Noting that the graph method relies on inverting a huge kernel matrix formed by both labeled and unlabeled samples, we originally introduce the Nyström method in the formulation to speed up the classification process. The presented semisupervised graphbased method is compared to stateoftheart support vector machines (SVMs) in the classification of hyperspectral data. The proposed method produces better classification maps which capture the intrinsic structure collectively revealed by labeled and unlabeled points. Good and stable accuracy is produced in illposed classification problems (high dimensional spaces and low number of labeled samples). Also, the introduction of the composite kernels framework drastically improves results, and the new fast formulation ranks almost linearly in the computational
Regularizing ad hoc retrieval scores
, 2005
"... The cluster hypothesis states: closely related documents tend to be relevant to the same request. We exploit this hypothesis directly by adjusting ad hoc retrieval scores from an initial retrieval so that topically related documents receive similar scores. We refer to this process as score regulariz ..."
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Cited by 47 (1 self)
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The cluster hypothesis states: closely related documents tend to be relevant to the same request. We exploit this hypothesis directly by adjusting ad hoc retrieval scores from an initial retrieval so that topically related documents receive similar scores. We refer to this process as score regularization. Score regularization can be presented as an optimization problem, allowing the use of results from semisupervised learning. We demonstrate that regularized scores consistently and significantly rank documents better than unregularized scores, given a variety of initial retrieval algorithms. We evaluate our method on two large corpora across a substantial number of topics.
Combining graph Laplacians for semisupervised learning
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 18
, 2005
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Semisupervised regression with cotraining style algorithms
, 2007
"... The traditional setting of supervised learning requires a large amount of labeled training examples in order to achieve good generalization. However, in many practical applications, unlabeled training examples are readily available but labeled ones are fairly expensive to obtain. Therefore, semisup ..."
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Cited by 43 (8 self)
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The traditional setting of supervised learning requires a large amount of labeled training examples in order to achieve good generalization. However, in many practical applications, unlabeled training examples are readily available but labeled ones are fairly expensive to obtain. Therefore, semisupervised learning has attracted much attention. Previous research on semisupervised learning mainly focuses on semisupervised classification. Although regression is almost as important as classification, semisupervised regression is largely understudied. In particular, although cotraining is a main paradigm in semisupervised learning, few works has been devoted to cotraining style semisupervised regression algorithms. In this paper, a cotraining style semisupervised regression algorithm, i.e. COREG, is proposed. This algorithm uses two regressors each labels the unlabeled data for the other regressor, where the confidence in labeling an unlabeled example is estimated through the amount of reduction in mean square error over the labeled neighborhood of that example. Analysis and experiments show that COREG can effectively exploit unlabeled data to improve regression estimates.
Dimensionality Reduction: A Comparative Review
, 2008
"... In recent years, a variety of nonlinear dimensionality reduction techniques have been proposed, many of which rely on the evaluation of local properties of the data. The paper presents a review and systematic comparison of these techniques. The performances of the techniques are investigated on arti ..."
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Cited by 42 (0 self)
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In recent years, a variety of nonlinear dimensionality reduction techniques have been proposed, many of which rely on the evaluation of local properties of the data. The paper presents a review and systematic comparison of these techniques. The performances of the techniques are investigated on artificial and natural tasks. The results of the experiments reveal that nonlinear techniques perform well on selected artificial tasks, but do not outperform the traditional PCA on realworld tasks. The paper explains these results by identifying weaknesses of current nonlinear techniques, and suggests how the performance of nonlinear dimensionality reduction techniques may be improved.
Higher order learning with graphs
 In ICML ’06: Proceedings of the 23rd international conference on Machine learning
, 2006
"... Recently there has been considerable interest in learning with higher order relations (i.e., threeway or higher) in the unsupervised and semisupervised settings. Hypergraphs and tensors have been proposed as the natural way of representing these relations and their corresponding algebra as the nat ..."
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Cited by 42 (0 self)
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Recently there has been considerable interest in learning with higher order relations (i.e., threeway or higher) in the unsupervised and semisupervised settings. Hypergraphs and tensors have been proposed as the natural way of representing these relations and their corresponding algebra as the natural tools for operating on them. In this paper we argue that hypergraphs are not a natural representation for higher order relations, indeed pairwise as well as higher order relations can be handled using graphs. We show that various formulations of the semisupervised and the unsupervised learning problem on hypergraphs result in the same graph theoretic problem and can be analyzed using existing tools. 1.
Online learning over graphs
 Proc. 22nd Int. Conf. Machine Learning
, 2005
"... We apply classic online learning techniques similar to the perceptron algorithm to the problem of learning a function defined on a graph. The benefit of our approach includes simple algorithms and performance guarantees that we naturally interpret in terms of structural properties of the graph, such ..."
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Cited by 41 (11 self)
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We apply classic online learning techniques similar to the perceptron algorithm to the problem of learning a function defined on a graph. The benefit of our approach includes simple algorithms and performance guarantees that we naturally interpret in terms of structural properties of the graph, such as the algebraic connectivity or the diameter of the graph. We also discuss how these methods can be modified to allow active learning on a graph. We present preliminary experiments with encouraging results. 1.
Ranking on graph data
 In ICML
, 2006
"... In ranking, one is given examples of order relationships among objects, and the goal is to learn from these examples a realvalued ranking function that induces a ranking or ordering over the object space. We consider the problem of learning such a ranking function when the data is represented as a ..."
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Cited by 41 (2 self)
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In ranking, one is given examples of order relationships among objects, and the goal is to learn from these examples a realvalued ranking function that induces a ranking or ordering over the object space. We consider the problem of learning such a ranking function when the data is represented as a graph, in which vertices correspond to objects and edges encode similarities between objects. Building on recent developments in regularization theory for graphs and corresponding Laplacianbased methods for classification, we develop an algorithmic framework for learning ranking functions on graph data. We provide generalization guarantees for our algorithms via recent results based on the notion of algorithmic stability, and give experimental evidence of the potential benefits of our framework. 1.