| Recently have witnessed the increasing interest and popularity on developing machine learning theories, algorithms and applications in the community of computer science. Among different machine learning methods, the statistical learning approach is a very promising direction, which aims to deal with the problem of finding predictive models based on given data samples by modeling them with certain probability distributions. It has found many different real-world applications in various areas including social computing, data mining, natural language processing, computer vision and signal processing. Within these empirical applications, it is common to observe differences across data points on various statistical features, or the statistical heterogeneity. However, many of them have been omitted in previous approaches.;This thesis aims to address the issue of handling the heterogeneous statistics among data in empirical machine learning problems, by exploring the heterogeneous properties among data samples from different perspectives. The basic idea is to group data samples based on different features according to empirical requirement, and the heterogeneous properties can be well captured accordingly. However, directly grouping data points can be nontrivial empirically. Because in some practical scenarios, the data points are heterogeneous with respect to latent perspectives. To tackle this issue, we proposed methods exploring the latent features and perform grouping simultaneously with an iterative statistical inference scheme. Another vital issue is that, how to determine the number of groups for data points. We further propose the Bayesian nonparametric approaches to handle this question effectively.;This thesis will be divided into seven parts, which are organized as following. The first part will provide a brief introduction on previous works on statistical learning with its applications, and the background knowledge on heterogeneous modeling. The second and third parts will introduce the application of heterogeneous modeling on the important application of image denoising, as a significant problem in the areas of computer vision and image processing. The forth part will further address the heterogeneous property on the dynamics of recommender systems based on the classical model of matrix factorization. The fifth part will propose another method on matrix factorization by capturing the feature sharing issue of user preference by exploring the heterogeneous property among latent user preferences. The sixth part will introduce a new model to capture the dynamics of heterogeneous modeling on the topic of dynamic topic models, which is an interesting issue in natural language processing. Here, we develop new Bayesian nonparametric modeling approach to capture the dynamics in grouping different words to explore topics among various documents. And finally, the seventh part will provide a conclusion of all these approaches, with some discussions on future works. |
