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.
Brefeld and Scheffer @cite_10 proposed to solve the problem of semi-supervised structured output prediction by learning in the space of input-output space, and using co-training method. This method is based on the assumption that the multiple structured output predictors should be consent with each other. Based on this assumption, the structural support vector machine is extended to the argued input-output space.
@cite_10
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Structured output prediction aims to learn a predictor to predict a structured output from a input data vector . The structured outputs include vector, tree, sequence, etc. We usually assume that we have a training set of input---output pairs to train the predictor. However, in many real-world applications, it is difficult to obtain the output for a input, and thus for many training input data points, the structured outputs are missing. In this paper, we discuss how to learn from a training set composed of some input---output pairs and some input data points without outputs. This problem is called semi-supervised structured output prediction. We propose a novel method for this problem by constructing a nearest neighbor graph from the input space to present the manifold structure and use it to regularize the structured output space directly. We define a slack structured output for each training data point and propose to predict it by learning a structured output predictor. The learning of both slack structured outputs and the predictor are unified within one single minimization problem. In this problem, we propose to minimize the structured loss between the slack structured outputs of neighboring data points and the prediction error measured by the structured loss. The problem is optimized by an iterative algorithm. Experiment results over three benchmark data sets show its advantage. The problem of learning a mapping between input and structured, interdependent output variables covers sequential, spatial, and relational learning as well as predicting recursive structures. Joint feature representations of the input and output variables have paved the way to leveraging discriminative learners such as SVMs to this class of problems. We address the problem of semi-supervised learning in joint input output spaces. The co-training approach is based on the principle of maximizing the consensus among multiple independent hypotheses; we develop this principle into a semi-supervised support vector learning algorithm for joint input output spaces and arbitrary loss functions. Experiments investigate the benefit of semi-supervised structured models in terms of accuracy and F1 score. In this paper, we present a supervised learning approach to training submodular scoring functions for extractive multidocument summarization. By taking a structured prediction approach, we provide a large-margin method that directly optimizes a convex relaxation of the desired performance measure. The learning method applies to all submodular summarization methods, and we demonstrate its effectiveness for both pairwise as well as coverage-based scoring functions on multiple datasets. Compared to state-of-the-art functions that were tuned manually, our method significantly improves performance and enables high-fidelity models with number of parameters well beyond what could reasonably be tuned by hand. Structured prediction is the problem of learning a function from structured inputs to structured outputs. Inspired by the recent successes of search-based structured prediction, we introduce a new framework for structured prediction called HC-Search. Given a structured input, the framework uses a search procedure guided by a learned heuristic H to uncover high quality candidate outputs and then uses a separate learned cost function C to select a final prediction among those outputs. We can decompose the regret of the overall approach into the loss due to H not leading to high quality outputs, and the loss due to C not selecting the best among the generated outputs. Guided by this decomposition, we minimize the overall regret in a greedy stagewise manner by first training H to quickly uncover high quality outputs via imitation learning, and then training C to correctly rank the outputs generated via H according to their true losses. Experiments on several benchmark domains show that our approach significantly outperforms the state-of-the-art methods.