With the development of modern digitization, increasingly more data emerge in almost all areas. It is worth emphasizing that not only does the quantity of the data increase, but also the number of data types, or the sources where data are collected, are boosted. Undoubtedly, more information can be exploited with the presence of more comprehensive data. Nevertheless, merging different data together also makes the analysis of them more challenging. There exist various forms of dependencies or interactions among multiple data. Therefore, working with these data goes much beyond traditional machine leaning tasks: e.g. classification or regression, where the output is a single scalar. In this dissertation, multiple data sets together are considered as structures, in which different dependencies can hence be modeled. In particular, structures are encoded within three forms by using: graphs, kernels and manifolds respectively, which can match different application domains. This dissertation goes through inference, learning and optimiza-
tion of structured data which are represented with different forms. Some existing work is reviewed while several new methods are put forward. In particular, to make the dissertation more practical, different methods were applied and evaluated on real-world application domains, including image segmentation, image annotation, protein function prediction, object-action relation modeling and 3D transformation estimation. Of course
the applicabilities of these methods go far beyond those presented in the dissertation. Meanwhile, this dissertation attempts to, with practical case studies, provide some main
principles or methodologies when confronting structured data, and empirical experience in above-mentioned domains should be easily transferred to other ones. Above all, the main contributions of this dissertation are several novel models and learning algorithms for structured outputs, including joint SVM and kernel generalized homogeneity analysis for multi-label learning, persistent sequential Monte Carlo for learning undirected graphical models. The study in this dissertation is expected to widen and/or deepen the understanding of relevant research.