On modeling order and structure with applications to computer vision and time series data

From the standpoint of computer vision systems, machine learning can offer effective methods for automating the acquisition of visual models, adapting parameters and representation, transforming signals to symbols, building trainable image-processing systems, focusing attention on target objects. From the opposite side, computer vision can present interesting and challenging problems for people working in machine learning. This dissertation focuses on developing new machine learning techniques for solving novel computer vision problems and modeling multivariate structure Poisson processes. In the first part of this work, we focus on a certain category of machine learning called ranking (ordinal regression and k-partite ranking) in which the data labels have an ordinal characteristic. We develop new algorithmic formulations for solving the ordinal regression problem using standard binary classification and regression techniques. We pose several computer vision problems, such as automatic focusing, age ranking/sorting, and estimating subpixel motion shifts in the ranking framework. We also investigate the applicability of a close relative of ordinal regression called as bipartite ranking for image retrieval. Furthermore, we analyze the theoretical properties of a natural extension of bipartite ranking called as k-partite ranking and study generalization properties under this setting. As noted above, the problem of estimating subpixel motion shifts can be posed in the ordinal regression setting. The estimated shifts can be used to align the images in a grid. The problem of superresolution reduces to estimating the unknown pixels in the grid. The second part of this dissertation is focused on building graphical models for performing superresolution/restoration from single and multiple images. The final part of this dissertation is the development of a new category of graphical models called Poisson networks for modeling structured multivariate structured Poisson processes. Applications for Poisson networks arise in several scenarios, namely, modeling neural spike trains for learning structure of data transmission in the brain, arrival times at nodes for learning the structure of queuing networks, etc. We develop techniques for sampling, inference and structure learning of Poisson networks.