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 so-called kernel trick with the large margin idea. There has been little use of these methods in an online setting suitable for real-time 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 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 real-world 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 co-variate shift. We also explore some potential future issues in transfer learning research.

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 boosting-based 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 high-quality 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.

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.

Empirical risk minimization offers well-known 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 trade-off 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 non-uniform combination of source risks can achieve much lower target error than standard empirical risk minimization. 1

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 two-sample 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 Kullback-Leibler divergence, we require sophisticated space partitioning and/or

We propose a multiple source domain adaptation method, referred to as Domain Adaptation Machine (DAM), to learn a robust decision function (referred to as target classifier) for label prediction of patterns from the target domain by leveraging a set of pre-computed classifiers (referred to as auxiliary/source classifiers) independently learned with the labeled patterns from multiple source domains. We introduce a new datadependent regularizer based on smoothness assumption into Least-Squares SVM (LS-SVM), which enforces that the target classifier shares similar decision values with the auxiliary classifiers from relevant source domains on the unlabeled patterns of the target domain. In addition, we employ a sparsity regularizer to learn a sparse target classifier. Comprehensive experiments on the challenging TRECVID 2005 corpus demonstrate that DAM outperforms the existing multiple source domain adaptation methods for video concept detection in terms of effectiveness and efficiency. 1.

The effectiveness of knowledge transfer using classification algorithms depends on the difference between the distribution that generates the training examples and the one from which test examples are to be drawn. The task can be especially difficult when the training examples are from one or several domains different from the test domain. In this paper, we propose a locally weighted ensemble framework to combine multiple models for transfer learning, where the weights are dynamically assigned according to a model’s predictive power on each test example. It can integrate the advantages of various learning algorithms and the labeled information from multiple training domains into one unified classification model, which can then be applied on a different domain. Importantly, different from many previously proposed methods, none of the base learning method is required to be specifically designed for transfer learning. We show the optimality of a locally weighted ensemble framework as a general approach to combine multiple models for domain transfer. We then propose an implementation of the local weight assignments by mapping the structures of a model onto the structures of the test domain, and then weighting each model locally according to its consistency with the neighborhood structure around the test example. Experimental results on text classification, spam filtering and intrusion detection data sets demonstrate significant improvements in classification accuracy gained by the framework. On a transfer learning task of newsgroup message categorization, the proposed locally weighted ensemble framework achieves 97 % accuracy when the best single model predicts correctly only on 73 % of the test examples. In summary, the improvement in accuracy is over 10 % and up to 30 % across different problems.

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 brain-computer interface, where strong non-stationarity effects can be seen between training and test sessions. c2000 Masashi Sugiyama, Matthias Krauledat, and Klaus-Robert Müller.

In many Web applications, such as blog classification and newsgroup classification, labeled data are in short supply. It often happens that obtaining labeled data in a new domain is expensive and time consuming, while there may be plenty of labeled data in a related but different domain. Traditional text classification approaches are not able to cope well with learning across different domains. In this paper, we propose a novel cross-domain text classification algorithm which extends the traditional probabilistic latent semantic analysis (PLSA) algorithm to integrate labeled and unlabeled data, which come from different but related domains, into a unified probabilistic model. We call this new model Topic-bridged PLSA, or TPLSA. By exploiting the common topics between two domains, we transfer knowledge across different domains through a topic-bridge to help the text classification in the target domain. A unique advantage of our method is its ability to maximally mine knowledge that can be transferred between domains, resulting in superior performance when compared to other state-of-the-art text classification approaches. Experimental evaluation on different kinds of datasets shows that our proposed algorithm can improve the performance of cross-domain text classification significantly.