Multi-task learning aims at learning multiple related but different tasks. In general, there are two ways for multi-task learning. One is to exploit the small set of labeled data from all tasks to learn a shared feature space for knowledge sharing. In this way, the focus is on the labeled training samples while the large amount of unlabeled data is not sufficiently considered. Another way has a focus on how to share model parameters among multiple tasks based on the original features space. Here, the question is whether it is possible to combine the advantages of both approaches and develop a method, which can simultaneously learn a shared subspace for multiple tasks and learn the prediction models in this subspace? To this end, in this paper, we propose a feature representation learning framework, which has the ability in combining the autoencoders, an effective way to learn good representation by using large amount of unlabeled data, and model parameter regularization methods into a unified model for multi-task learning. Specifically, all the tasks share the same encoding and decoding weights to find their latent feature representations, based on which a regularized multi-task softmax regression method is used to find a distinct prediction model for each task. Also, some commonalities are considered in the prediction models according to the relatedness of multiple tasks. There are several advantages of the proposed model: 1) it can make full use of large amount of unlabeled data from all the tasks to learn satisfying representations, 2) the learning of distinct prediction models can benefit from the success of autoencoder, 3) since we incorporate the labeled information into the softmax regression method, so the learning of feature representation is indeed in a semi-supervised manner. Therefore, our model is a semi-supervised autoencoder for multi-task learning (SAML for short). Finally, extensive experiments on three real-world data sets demonstrate the effectiveness of the proposed framework. Moreover, the feature representation obtained in this model can be used by other methods to obtain improved results.

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