When labeled examples are limited and difficult to obtain, transfer learning employs knowledge from a source domain to improve learning accuracy in the target domain. However, the assumption made by existing approaches, that the marginal and conditional probabilities are directly related between source and target domains, has limited applicability in either the original space or its linear transformations. To solve this problem, we propose an adaptive kernel approach that maps the marginal distribution of targetdomain and source-domain data into a common kernel space, and utilize a sample selection strategy to draw conditional probabilities between the two domains closer. We formally show that under the kernel-mapping space, the difference in distributions between the two domains is bounded; and the prediction error of the proposed approach can also be bounded. Experimental results demonstrate that the proposed method outperforms both traditional inductive classifiers and the state-of-the-art boosting-based transfer algorithms on most domains, including text categorization and web page ratings. In particular, it can achieve around 10 % higher accuracy than other approaches for the text categorization problem. The source code and datasets are available from the authors.

Transferring knowledge from one domain to another is challenging due to a number of reasons. Since both conditional and marginal distribution of the training data and test data are non-identical, model trained in one domain, when directly applied to a different domain, is usually low in accuracy. For many applications with large feature sets, such as text document, sequence data, medical data, image data of different resolutions, etc. two domains usually do not contain exactly the same features, thus introducing large numbers of “missing values”when considered over the union of features from both domains. In other words, its marginal distributions are at most overlapping. In the same time, these problems are usually high dimensional, such as, several thousands of features. Thus, the combination of high

Transferring knowledge from one domain to another is challenging due to a number of reasons. Since both conditional and marginal distribution of the training data and test data are non-identical, model trained in one domain, when directly applied to a different domain, is usually low in accuracy. For many applications with large feature sets, such as text document, sequence data, medical data, image data of different resolutions, etc. two domains usually do not contain exactly the same features, thus introducing large numbers of “missing values”when considered over the union of features from both domains. In other words, its marginal distributions are at most overlapping. In the same time, these problems are usually high dimensional, such as, several thousands of features. Thus, the combination of high

Abstract. The basis assumption that “training and test data drawn from the same distribution ” is often violated in reality. In this paper, we propose one common solution to cover various scenarios of learning under “different but related distributions ” in a single framework. Explicit examples include (a) sample selection bias between training and testing data, (b) transfer learning or no labeled data in target domain, and (c) noisy or uncertain training data. The main motivation is that one could ideally solve as many problems as possible with a single approach. The proposed solution extends graph transduction using the maximum margin principle over unlabeled data. The error of the proposed method is bounded under reasonable assumptions even when the training and testing distributions are different. Experiment results demonstrate that the proposed method improves the traditional graph transduction by as much as 15 % in accuracy and AUC in all common situations of distribution difference. Most importantly, it outperforms, by up to 10 % in accuracy, several state-of-art approaches proposed to solve specific category of distribution difference, i.e, BRSD [1] for sample selection bias, CDSC [2] for transfer learning, etc. The main claim is that the adaptive graph transduction is a general and competitive method to solve distribution differences implicitly without knowing and worrying about the exact type. These at least include sample selection bias, transfer learning, uncertainty mining, as well as those alike that are still not studied yet.Thesourcecodeanddatasetsareavailablefromtheauthors. 1