基于马氏抽样的机器学习理论与算法研究

随着计算机技术的飞速发展，人们收集数据、存储数据的能力得到了极大的提高。无论是科学研究, 还是社会生活的各个领域中都积累了大量的数据, 对这些数据进行分析以发掘出数据中蕴含的有用信息，几乎成为所有领域的共同需求和要面临的挑战。在多年来对非独立同分布数据下机器学习理论和算法研究的基础上，我们提出了对数据进行马氏抽样以便更好发掘数据中有用信息的思想和方法。本项目旨在通过研究马氏抽样下机器学习算法的一致性、收敛速率和泛化性能，建立马氏抽样下机器学习的理论框架，进而对不同学习问题建立具有比较好的泛化性、稳定性和稀疏性等学习性能的马氏抽样方法，并将研究成果应用到数据挖掘的实际问题中，为数据挖掘，特别是海量数据挖掘提供数据分析的新技术和新方法。

With the rapid development of computer technology, the ability of collecting data and storing data has been improved dramatically. Both the science research and other fields of public life have accumulated a large number of data. Analyzing these data and exploring the useful information from these data have been the joint demand and the challenge. In order to better find the useful information from the data set, we introduce the method and ideal of Markov sampling from the data set based on many years' study on the theory and algorithm of machine learning with non-i.i.d. samples. The goal of this project is to establish the framwork of machine learning theory for Markov sampling by studying the consistency, convergence rate and generalization ability of machine learning algorithms based on Markov sampling. We will establish the Markov sampling method that has better learning properties such as better generalization ability, better stable property and better sparse property for different learning problems, and then apply these research's results to the application domains of data mining. Our aim is to present some new techniques and some new methods of data analysis for the data mining of massive data.