Discriminative learning when training and test data belong to different distributions is a challenging and complex task. Often times we have very few or no labeled data from the test or target distribution but may have plenty of labeled data from multiple related sources with different distributions. The difference in distributions may be in both marginal and conditional probabilities. Most of the existing domain adaptation work focuses on the marginal probability distribution difference between the domains, assuming that the conditional probabilities are similar. However in many real world applications, conditional probability distribution differences are as commonplace as marginal probability differences. In this paper we propose a two-stage domain adaptation methodology which combines weighted data from multiple sources based on marginal probability differences (first stage) as well as conditional probability differences (second stage), with the target domain data. The weights for minimizing the marginal probability differences are estimated independently, while the weights for minimizing conditional probability differences are computed simultaneously by exploiting the potential interaction among multiple sources. We also provide a theoretical analysis on the generalization performance of the proposed multi-source domain adaptation formulation using the weighted Rademacher complexity measure. Empirical comparisons with existing state-of-the-art domain adaptation methods using three real-world datasets demonstrate the effectiveness of the proposed approach.