In this paper, we study the problem of semi-supervised structured output prediction, which aims to learn predictors for structured outputs, such as sequences, tree nodes, vectors, etc., from a set of data points of both inputoutput pairs and single inputs without outputs. The traditional methods to solve this problem usually learns one single predictor for all the data points, and ignores the variety of the different data points. Different parts of the data set may have different local distributions, and requires different optimal local predictors. To overcome this disadvantage of existing methods, we propose to learn different local predictors for neighborhoods of different data points, and the missing structured outputs simultaneously. In the neighborhood of each data point, we proposed to learn a linear predictor by minimizing both the complexity of the predictor and the upper bound of the structured prediction loss. The minimization is conducted by gradient descent algorithms. Experiments over four benchmark data sets, including DDSM mammography medical images, SUN natural image data set, Cora research paper data set, and Spanish news wire article sentence data set, show the advantages of the proposed method.
@cite_26 proposed a hybrid method to solve the problem of semi-supervised structured output learning. This method combines both the generative and discriminative methods. The objective of this method is composed of log-linear forms of both discriminative structured predictor and generative model. The generative model is used to incorporate unlabeled data points. The discriminant functions is enhanced by the unlabeled data points provided by the generative model.
@cite_26
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This paper proposes a framework for semi-supervised structured output learning (SOL), specifically for sequence labeling, based on a hybrid generative and discriminative approach. We define the objective function of our hybrid model, which is written in log-linear form, by discriminatively combining discriminative structured predictor(s) with generative model(s) that incorporate unlabeled data. Then, unlabeled data is used in a generative manner to increase the sum of the discriminant functions for all outputs during the parameter estimation. Experiments on named entity recognition (CoNLL-2003) and syntactic chunking (CoNLL-2000) data show that our hybrid model significantly outperforms the stateof-the-art performance obtained with supervised SOL methods, such as conditional random fields (CRFs).