Bayesian Prediction and Regression from Visual Data

Abstract

This dissertation proposes a new high dimensional regression / prediction method for diverse visual data pairs. In contrast to other regression / prediction methods, the proposed method focuses on the case where output responses are on a complex high dimensional manifold, such as images. In handling the complex data, the latent space embedding the information of the data is used for efficient regression / prediction. The dimensionality reduction methods into the latent space and the regression/prediction methods are designed as a Bayesian framework. For the prediction problem, the dissertation proposes a method to extract latent semantics on motion dynamics given in visual sequences. To this end, a Bayesian inference model is developed to capture the regional and temporal semantics of the dynamics data. The proposed Bayesian model is a hierarchical fusion of Gaussian mixture model and topic mixture model. It finds regional pattern information through topic mixture model and derives temporal co-occurrence of regional patterns through Gaussian mixture model. To infer the proposed model, the dissertation proposes a new sampling method that enables efficient inference. For the regression problem, we propose a method that makes a regression in the latent space for general and complex visual data pairs. This allows the latent space to imply the essential properties of the data pairs required for regression. For the purpose, a regression model is designed so that the regression in latent space should coincide with the regression in data space. The whole models are designed as Bayesian framework, and inferred by variational autoencoder framework.