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Multi-source unsupervised domain adaptation (MS-UDA) for sentiment analysis (SA) aims to leverage useful information in multiple source domains to help do SA in an unlabeled target domain that has no supervised information. Existing algorithms of MS-UDA either only exploit the shared features, i.e., the domain-invariant information, or based on some weak assumption in NLP, e.g., smoothness assumption. To avoid these problems, we propose two transfer learning frameworks based on the multi-source domain adaptation methodology for SA by combining the source hypotheses to derive a good target hypothesis. The key feature of the first framework is a novel Weighting Scheme based Unsupervised Domain Adaptation framework (WS-UDA), which combine the source classifiers to acquire pseudo labels for target instances directly. While the second framework is a Two-Stage Training based Unsupervised Domain Adaptation framework (2ST-UDA), which further exploits these pseudo labels to train a target private extractor. Importantly, the weights assigned to each source classifier are based on the relations between target instances and source domains, which measured by a discriminator through the adversarial training. Furthermore, through the same discriminator, we also fulfill the separation of shared features and private features. Experimental results on two SA datasets demonstrate the promising performance of our frameworks, which outperforms unsupervised state-of-the-art competitors.