Learning sparse graphical models for data restoration and multi-label classification

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Sparse probabilistic graphical models play an important role in structured prediction when the dependency structure is unknown. By inducing sparsity over edge parameters, a typical sparse graphical model can combine structure learning and parameter estimation under a unified optimization framework. In this thesis, we propose three specific sparse graphical models accompanied by their applications in data restoration and multi-label classification respectively. For the data restoration task, we propose random mixed field (RMF) model to explore mixed-attribute correlations among data. The RMF model is capable of handling mixed-attribute data denoising and imputation simultaneously. Meanwhile, RMF employs a structured mean-field variational approach to decouple continuous-discrete interactions to achieve approximate inference. The effectiveness of this model is evaluated on both synthetic and real-world data. For the multi-label classification task, we propose correlated logistic model (CorrLog) and conditional graphical lasso (CGL), to learn conditional label correlations. (1) The CorrLog model characterizes pairwise label correlations via scalar parameters, thus effects in an explicit (or direct) fashion. More specifically, CorrLog extends conventional logistic regression by jointly modelling label correlations. In addition, elastic-net regularization is employed to induce sparsity over the scalar parameters that define label correlations. CorrLog can be efficiently learned by regularized maximum pseudo likelihood estimation which enjoys a satisfying generalization bound. Besides, message passing algorithm is applied to solve the multi-label prediction problem. (2) The CGL model further leverages features in modelling pairwise label correlations in terms of parametric functions of the input features, which effects in an implicit (or indirect) fashion. In general, CGL provides a unified Bayesian framework for structure and parameter learning conditioned on input features. We formulate the multi-label prediction as CGL inference problem, which is solved by a mean field variational approach. Meanwhile, CGL learning is efficient after applying the maximum a posterior (MAP) methodology and solved by a proximal gradient procedure. The effectiveness of CorrLog and CGL are evaluated on several benchmark multi-label classification datasets.
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