This paper presents an analysis of representations for domain adaptation, focusing on how to adapt classifiers from a source domain to a target domain with different distributions. The paper introduces a formalization of a bound on the target generalization error of a classifier trained from labeled data in the source domain. The key idea is that a common representation can make two domains appear similar, enabling effective domain adaptation. The problem setup involves an instance set X, a label set {0,1}, and a feature set Z. A representation function R maps instances to features, and a hypothesis class H is used to define classifiers. The paper assumes that there exists a hypothesis h in H that performs well on both domains. The theorem provides a bound on the target error of a classifier trained on the source domain, considering the training error, domain distance, and a small λ. The paper also introduces a method to compute the domain distance between distributions, using a proxy based on a classifier that discriminates between points generated by source and target distributions. An example application is adapting a part-of-speech tagger from financial to biomedical domains. The procedure involves choosing a representation R, training a classifier, and measuring relevant terms of the bound. The representation is built using structural correspondence learning, finding domain-independent features and representing others based on their co-occurrence with these features. Empirical results show that the SCL representation effectively captures the structure of both domains. The paper contributes an analysis of classification problems with different domain distributions and provides an upper bound on the generalization of classifiers trained on source domains and applied to target domains.This paper presents an analysis of representations for domain adaptation, focusing on how to adapt classifiers from a source domain to a target domain with different distributions. The paper introduces a formalization of a bound on the target generalization error of a classifier trained from labeled data in the source domain. The key idea is that a common representation can make two domains appear similar, enabling effective domain adaptation. The problem setup involves an instance set X, a label set {0,1}, and a feature set Z. A representation function R maps instances to features, and a hypothesis class H is used to define classifiers. The paper assumes that there exists a hypothesis h in H that performs well on both domains. The theorem provides a bound on the target error of a classifier trained on the source domain, considering the training error, domain distance, and a small λ. The paper also introduces a method to compute the domain distance between distributions, using a proxy based on a classifier that discriminates between points generated by source and target distributions. An example application is adapting a part-of-speech tagger from financial to biomedical domains. The procedure involves choosing a representation R, training a classifier, and measuring relevant terms of the bound. The representation is built using structural correspondence learning, finding domain-independent features and representing others based on their co-occurrence with these features. Empirical results show that the SCL representation effectively captures the structure of both domains. The paper contributes an analysis of classification problems with different domain distributions and provides an upper bound on the generalization of classifiers trained on source domains and applied to target domains.