鉴于大家对机械课程设计十分关注，我们编辑小组在此为大家搜集整理了“贝叶斯分析方法研究”一文，供大家参考学习!
摘 要机器学习作为一门人工智能的科学自20世纪50年代被提出以来，经过人们的不断研究，已形成了一套科学系统的理论。机器学习中一个很重要的步骤是特征的选择与提取，原始特征的数量可能很大，或者说样本处在一个高维空间中，我们需要找到一个合理的方法，降低特征数量的同时，尽量减少原特征中包含信息的损失，因子分析法就是这样一种降维的方法。然而由于因子分析模型中存在不可观测的隐变量，普通的极大似然法很难得到其参数的估计。贝叶斯理论提供了一种计算各变量后验概率的方法，这种方法基于假设的先验概率和观测到的数据，可以得到模型各变量的后验概率。本文的工作正是在这种研究背景下展开的。在前人工作的基础上，本文着重研究了如何运用变分贝叶斯算法推导出因子分析法的贝叶斯后验分布公式。归纳起来，本文的主要内容包括以下四个方面：*简要介绍贝叶斯机器学习的基础知识，包括贝叶斯定理，贝叶斯估计和几种先验分布。*简要介绍因子分析模型，分析其降维的机理。*为估计因子分析模型中的参数，引入EM算法和变分贝叶斯算法，以解决模型中存在隐变量的问题。*推导因子分析法的贝叶斯后验分布公式，并用Matlab编程实现，通过合成数据检验理论的正确性最后，我们对全文工作进行了总结，并指出今后需要进一步研究的一些问题。关键词：因子分析法 贝叶斯理论 后验分布 EM算法 变分贝叶斯算法 ABSTRACTAs a kind of artificial intelligence science, machine learning was proposed in the 1950’s and has formed a scientific and systematic theory. A very important step in machine learning is feature extraction and selection. The number of original features may be huge, or we can say that the sample is in a high dimensional space. So we need to find a reasonable approach which can not only reduce the number of observed variables, but also minimize the loss of the information contained in the original features. Factor analysis is such a dimension reduction method. However, because of the existence of unobserved hidden variables in the factor analysis model, the estimation of parameters using maximum likelihood solution becomes intractable. The Bayesian theory provides a solution to compute the posterior probabilistic of variables. Based on the assumption of prior probabilistic and the observed data, it can find the posterior probabilistic of all variables in the model. Based on previous work, this paper focuses on the derivation of the Bayesian posterior distribution of the parameters in factor analysis model via the Variational Bayesian algorithm. The main content of this paper is summarized as follows:完成 实现implementation* Briefly introduce the basic knowledge of Bayesian machine learning, including the Bayesian method, Bayesian inference and the choice of prior.* Briefly introduce the factor analysis model.* Introduce EM algorithm and Variational Bayesian algorithm for the estimation of parameters, in order to solve the problem of hidden variable.* Derive the Bayesian posterior distribution of the parameters, and code the algorithm with Matlab, which is validated by experiments using synthetic data.Finally, we conclude the paper with a summary and advance some suggestions for fur
