Computer Computer Infect Computer Viruses Prevent Infection Diseases Vaccines System Updates Human infect Human Prevent Infection Cause Malfunction Cause Disfunction

Transfer learning allows knowledge to be extracted from auxiliary domains and be used to enhance learning in a target domain. For transfer learning to be successful, it is critical to find the similarity between auxiliary and target domains, even when such mappings are not obvious. In this paper, we present a novel algorithm for finding the structural similarity between two domains, to enable transfer learning at a structured knowledge level. In particular, we address the problem of how to learn a non-trivial structural similarity mapping between two different domains when they are completely different on the representation level. This problem is challenging because we cannot directly compare features across domains. Our algorithm extracts the structural features within each domain and then maps the features into the Reproducing Kernel Hilbert Space (RKHS), such that the “structural dependencies” of features across domains can be estimated by kernel matrices of the features within each domain. By treating the analogues from both domains as equivalent, we can transfer knowledge to achieve a better understanding of the domains and improved performance for learning. We validate our approach on a large number of transfer learning scenarios constructed from a real world dataset. Introduction and Motivation Re-using knowledge across different learning tasks (domains) has long been addressed in the machine learning literature (Thrun 1998; Caruana 1997; Daumé III 2006; Dai 2008; Blitzer 2006). Existing research on this issue usually assume that the tasks are related on the low level, i.e. they share the same feature space or the same parametric family of models, such that knowledge transfer can be achieved by re-using weighted samples across tasks, finding a shared intermediate representation, or learning constraints (informative priors) on the model parameters. However, examining knowledge transfer in human intelligence, we could find that human beings do not rely on such low-level relatedness to transfer knowledge across domains. Namely, we human beings are able to make analogy Copyright c © 2011, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. across different domains by resolving the high level (structural) similarities even when the learning tasks (domains) are seemingly irrelevant. For example, we can easily understand the analogy between debugging for computer viruses and diagnosing human diseases. Even though the computer viruses (harmful codes) themselves have nothing in common with bacteria or germs, and the computer systems is totally different from our bodies, we can still make the analogy base on the following structural similarities: 1. Computer viruses cause malfunction of computers. Diseases cause disfunction of the human body. 2. Computer viruses spread among computers through the networks. Infectious diseases spread among people through various interactions. 3. System updates help computers avoid certain viruses. Vaccines help human beings avoid certain diseases. Understanding of these structural similarities helps us abstract away the details specific to the domains, and build a mapping between the abstractions (see Figure 1). The mapping builds on the high level structural relatedness of the two domains, instead of their low level “literal similarities”. In other words, the attributes of the “computer” and the “human” themselves do not matter to the mapping, whereas their relationships to other entities in their own domains matter. This is reminiscent of the learning-by-analogy paradigm in early endeavors in intelligent planing and problem solving. However, many previous operational systems in computational analogy, such as case-based reasoning, have used a simple similarity function between an old and new problem domain, whereby the features in the two domains are identical, albeit weighted. This similarity measure cannot handle some more intuitive cases of human problem solving, such as the above example, in which the similarity between the domains should be measured on the structural level. And such a “structural similarity” can only be determined if we can correctly identify analogues across completely different representation spaces. On the other hand, in cognitive science, analogical learning indeed involves developing a set of mappings between features from different domains. Such a need is captured in structure mapping theory (Falkenhainer 1989; Gentner 1990) of analogical reasoning, which argued for deep reComputer Computer Infect Computer Viruses Prevent Infection Diseases Vaccines System Updates Human infect Human Prevent Infection Cause Malfunction Cause Disfunction Figure 1: We can make the analogy between debugging for computer viruses and diagnosing human diseases based on structural similarities. The dash lines bridge analogues across domains. lational similarity rather than superficial similarity. However, an operational computational theory has been lacking for how to come up with the mapping function. We try to fill this gap in this paper. In this paper, we present a framework of transfer learning by structural analogy, which builds on functional space embedding of distributions (Smola 2007). Specifically, we address transfer learning in a setting that the source domain and target domain are using completely different representation spaces. As we cannot directly compare features across domains, we extract the structural information of the features within each domain by mapping the features into the Reproducing Kernel Hilbert Space (RKHS), such that the “structural dependencies” of features across domains can be estimated by kernel matrices of the features within each domain (Smola 2007). Hence the learning process is formulated as simultaneously selecting and associating features from both domains to maximize the dependencies between the selected features and response variables (labels), as well as between the selected features from both domains. With the learned cross-domain mapping, a structural similarity between the two domains can be readily computed, which can be used in place of simple similarity measures in computational analogy systems such as case based reasoning. By treating the analogues from both domains as equivalent, we can transfer knowledge to achieve a better understanding of the domains, e.g. better accuracy in classification tasks.