Research On Bayesian Nonparametric Modeling Methods And Applications For Statistical Sparse Learning

Statical sparse learning method is an interdisciplinary area in artificial intelligence, applied statistics and visual perception, and is one of the hot topics in machine learning researching. The general Bayesian learning framework is an appropriate model for un-certainty representation, which denotes all forms of uncertainty with probability, learning and inference, combining the prior knowledge and sample information. Comparing with other methods, Bayesian nonparametric method represents the uncertainty with stochastic process, which takes the benefit of the unlimited parameters and unbounded dimensions to reduce the constraints on the parameter assumption and avoid over-fitting implicitly. The characteristic information are learned and inferred by Bayesian theorem based on the explanation of the model, which provides an adaptive method for model selection. There-for, it is important to study the modeling methods and inference process of statical sparse learning based on Bayesian nonparametric. Furthermore, sparse learning is a natural rep-resentation in vision perception. The studies of statical sparse learning based on Bayesian nonparametric applying in vision tasks help to identify the properties and advantages of the methods, and on the other hand, the applications provide platforms for validation.The main contents of this dissertation are focused on Bayesian nonparametric statical sparse learning. Some key issues of nonparametric sparse modeling at the perspective of probability measure are studied and validated by vision tasks under the Bayesian statistical learning framework. The dissertation makes some creative researches on the following aspects:1. Based on the analysis of the problems in the statistical learning theorem, the model construction, learning methods and inference mechanism of Bayesian nonparametric are studied, and to our known, the sparse expression of Bayesian nonparametric is firstly stud-ied in domestic research and this is the first review in Chinese.2. Based on the extent of sparse vector function form, a Bayesian nonparametric method for adaptive sparse linear expression is proposed. Modeling method based on the discrete mixed prior beta process for sparse express could make observation data self adapt the sparse degree according to the known measure matrix. The Laplace prior in the model which is expressed by an Gaussian probability form could make competitive calculation, as well as it has state of the art sparseness. The experiments for reconstruction of the uniform spikes signal outperform other methods in terms of reconstruction error. The experiments for the recognition of handwriting digital sets show the effectiveness of the algorithm.3. According to the limitation of pre-decided dimension in dictionary learning mod-eling, a dictionary learning method based on Bayesian nonparametric is presented, taking advantages of the Gaussian process fitting the clustering problem, especially for the im-age denoising problem. In the model, the measure matrix is constructed by column limited Gaussian dictionary from the sample set, which provides the reliability of the dictionary learning and the optimization of the sparse expression results. The experiments show the effectiveness and flexibility, and the reliable prediction can be achieved by careful hyper-parameters selections.4. On the basis of a deep analysis on the bottlenecks that Bayesian nonparametric has met in clustering problem, different methods are proposed for video data clustering and high-dimensional space clustering. We model the background subtraction problem with the Dirichlet process mixture, which constantly adapts both the parameters and the number of components of the mixture to the scene, and the experiment results confirm the feasibility and effectiveness. For the high-dimensional space clustering, we present a the Polya tree clustering method, which firstly abstracts the feature of the data and forms the sparse high-dimension attribution matrix, and then clusters are induced during the construction of the Polya tree. The experiments working on CIFAR images data set get good performance.