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135
Online Learning with Kernels
, 2003
"... Kernel based algorithms such as support vector machines have achieved considerable success in various problems in the batch setting where all of the training data is available in advance. Support vector machines combine the socalled kernel trick with the large margin idea. There has been little u ..."
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Cited by 2084 (126 self)
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Kernel based algorithms such as support vector machines have achieved considerable success in various problems in the batch setting where all of the training data is available in advance. Support vector machines combine the socalled kernel trick with the large margin idea. There has been little use of these methods in an online setting suitable for realtime applications. In this paper we consider online learning in a Reproducing Kernel Hilbert Space. By considering classical stochastic gradient descent within a feature space, and the use of some straightforward tricks, we develop simple and computationally efficient algorithms for a wide range of problems such as classification, regression, and novelty detection. In addition to allowing the exploitation of the kernel trick in an online setting, we examine the value of large margins for classification in the online setting with a drifting target. We derive worst case loss bounds and moreover we show the convergence of the hypothesis to the minimiser of the regularised risk functional. We present some experimental results that support the theory as well as illustrating the power of the new algorithms for online novelty detection. In addition
A Survey on Transfer Learning
"... A major assumption in many machine learning and data mining algorithms is that the training and future data must be in the same feature space and have the same distribution. However, in many realworld applications, this assumption may not hold. For example, we sometimes have a classification task i ..."
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Cited by 195 (18 self)
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A major assumption in many machine learning and data mining algorithms is that the training and future data must be in the same feature space and have the same distribution. However, in many realworld applications, this assumption may not hold. For example, we sometimes have a classification task in one domain of interest, but we only have sufficient training data in another domain of interest, where the latter data may be in a different feature space or follow a different data distribution. In such cases, knowledge transfer, if done successfully, would greatly improve the performance of learning by avoiding much expensive data labeling efforts. In recent years, transfer learning has emerged as a new learning framework to address this problem. This survey focuses on categorizing and reviewing the current progress on transfer learning for classification, regression and clustering problems. In this survey, we discuss the relationship between transfer learning and other related machine learning techniques such as domain adaptation, multitask learning and sample selection bias, as well as covariate shift. We also explore some potential future issues in transfer learning research.
Boosting for transfer learning
 In ICML
, 2007
"... Traditional machine learning makes a basic assumption: the training and test data should be under the same distribution. However, in many cases, this identicaldistribution assumption does not hold. The assumption might be violated when a task from one new domain comes, while there are only labeled d ..."
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Cited by 93 (11 self)
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Traditional machine learning makes a basic assumption: the training and test data should be under the same distribution. However, in many cases, this identicaldistribution assumption does not hold. The assumption might be violated when a task from one new domain comes, while there are only labeled data from a similar old domain. Labeling the new data can be costly and it would also be a waste to throw away all the old data. In this paper, we present a novel transfer learning framework called TrAdaBoost, which extends boostingbased learning algorithms (Freund & Schapire, 1997). TrAdaBoost allows users to utilize a small amount of newly labeled data to leverage the old data to construct a highquality classification model for the new data. We show that this method can allow us to learn an accurate model using only a tiny amount of new data and a large amount of old data, even when the new data are not sufficient to train a model alone. We show that TrAdaBoost allows knowledge to be effectively transferred from the old data to the new. The effectiveness of our algorithm is analyzed theoretically and empirically to show that our iterative algorithm can converge well to an accurate model.
Discriminative learning for differing training and test distributions
 In ICML
, 2007
"... We address classification problems for which the training instances are governed by a distribution that is allowed to differ arbitrarily from the test distribution—problems also referred to as classification under covariate shift. We derive a solution that is purely discriminative: neither training ..."
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Cited by 78 (7 self)
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We address classification problems for which the training instances are governed by a distribution that is allowed to differ arbitrarily from the test distribution—problems also referred to as classification under covariate shift. We derive a solution that is purely discriminative: neither training nor test distribution are modeled explicitly. We formulate the general problem of learning under covariate shift as an integrated optimization problem. We derive a kernel logistic regression classifier for differing training and test distributions. 1.
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 72 (37 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.
Learning bounds for domain adaptation
 In Advances in Neural Information Processing Systems
, 2008
"... Empirical risk minimization offers wellknown learning guarantees when training and test data come from the same domain. In the real world, though, we often wish to adapt a classifier from a source domain with a large amount of training data to different target domain with very little training data. ..."
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Cited by 62 (7 self)
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Empirical risk minimization offers wellknown learning guarantees when training and test data come from the same domain. In the real world, though, we often wish to adapt a classifier from a source domain with a large amount of training data to different target domain with very little training data. In this work we give uniform convergence bounds for algorithms that minimize a convex combination of source and target empirical risk. The bounds explicitly model the inherent tradeoff between training on a large but inaccurate source data set and a small but accurate target training set. Our theory also gives results when we have multiple source domains, each of which may have a different number of instances, and we exhibit cases in which minimizing a nonuniform combination of source risks can achieve much lower target error than standard empirical risk minimization. 1
A Hilbert space embedding for distributions
 In Algorithmic Learning Theory: 18th International Conference
, 2007
"... Abstract. We describe a technique for comparing distributions without the need for density estimation as an intermediate step. Our approach relies on mapping the distributions into a reproducing kernel Hilbert space. Applications of this technique can be found in twosample tests, which are used for ..."
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Cited by 56 (28 self)
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Abstract. We describe a technique for comparing distributions without the need for density estimation as an intermediate step. Our approach relies on mapping the distributions into a reproducing kernel Hilbert space. Applications of this technique can be found in twosample tests, which are used for determining whether two sets of observations arise from the same distribution, covariate shift correction, local learning, measures of independence, and density estimation. Kernel methods are widely used in supervised learning [1, 2, 3, 4], however they are much less established in the areas of testing, estimation, and analysis of probability distributions, where information theoretic approaches [5, 6] have long been dominant. Recent examples include [7] in the context of construction of graphical models, [8] in the context of feature extraction, and [9] in the context of independent component analysis. These methods have by and large a common issue: to compute quantities such as the mutual information, entropy, or KullbackLeibler divergence, we require sophisticated space partitioning and/or
Direct importance estimation with model selection and its application to covariate shift adaptation
 In NIPS
, 2008
"... A situation where training and test samples follow different input distributions is called covariate shift. Under covariate shift, standard learning methods such as maximum likelihood estimation are no longer consistent—weighted variants according to the ratio of test and training input densities ar ..."
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Cited by 45 (9 self)
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A situation where training and test samples follow different input distributions is called covariate shift. Under covariate shift, standard learning methods such as maximum likelihood estimation are no longer consistent—weighted variants according to the ratio of test and training input densities are consistent. Therefore, accurately estimating the density ratio, called the importance, is one of the key issues in covariate shift adaptation. A naive approach to this task is to first estimate training and test input densities separately and then estimate the importance by taking the ratio of the estimated densities. However, this naive approach tends to perform poorly since density estimation is a hard task particularly in high dimensional cases. In this paper, we propose a direct importance estimation method that does not involve density estimation. Our method is equipped with a natural cross validation procedure and hence tuning parameters such as the kernel width can be objectively optimized. Simulations illustrate the usefulness of our approach. 1
Graph Kernels
, 2007
"... We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexit ..."
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Cited by 42 (4 self)
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We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n 6) to O(n 3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixedpoint methods that take O(dn 3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for ddimensional edge kernels, and O(n 4) in the infinitedimensional case; on sparse graphs these algorithms only take O(n 2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to Rconvolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semidefinite.
Domain Adaptation via Transfer Component Analysis
"... Domain adaptation solves a learning problem in a target domain by utilizing the training data in a different but related source domain. Intuitively, discovering a good feature representation across domains is crucial. In this paper, we propose to find such a representation through a new learning met ..."
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Cited by 41 (15 self)
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Domain adaptation solves a learning problem in a target domain by utilizing the training data in a different but related source domain. Intuitively, discovering a good feature representation across domains is crucial. In this paper, we propose to find such a representation through a new learning method, transfer component analysis (TCA), for domain adaptation. TCA tries to learn some transfer components across domains in a Reproducing Kernel Hilbert Space (RKHS) using Maximum Mean Discrepancy (MMD). In the subspace spanned by these transfer components, data distributions in different domains are close to each other. As a result, with the new representations in this subspace, we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain. The main contribution of our work is that we propose a novel feature representation in which to perform domain adaptation via a new parametric kernel using feature extraction methods, which can dramatically minimize the distance between domain distributions by projecting data onto the learned transfer components. Furthermore, our approach can handle large datsets and naturally lead to outofsample generalization. The effectiveness and efficiency of our approach in are verified by experiments on two realworld applications: crossdomain indoor WiFi localization and crossdomain text classification. 1