Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on mixture model which is known as the EM algorithm where the parameters of the mixture model are usually estimated into a maximum likelihood estimation framework. Bayesian approach for finite and infinite Gaussian mixture model generates point estimates for all variables as well as associated uncertainty in the form of the whole estimates' posterior distribution. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in Bayesian inference for finite and infinite Gaussian mixture model in order to seamlessly introduce their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning this field and given the paucity of scope to present this discussion, e.g., the separated analysis of the generation of Dirichlet samples by stick-breaking and Polya's Urn approaches. We refer the reader to literature in the field of the Dirichlet process mixture model for a much detailed introduction to the related fields. Some excellent examples include (Frigyik et al., 2010; Murphy, 2012; Gelman et al., 2014; Hoff, 2009). This survey is primarily a summary of purpose, significance of important background and techniques for Gaussian mixture model, e.g., Dirichlet prior, Chinese restaurant process, and most importantly the origin and complexity of the methods which shed light on their modern applications. The mathematical prerequisite is a first course in probability. Other than this modest background, the development is self-contained, with rigorous proofs provided throughout.
翻译:集束化已成为机器学习的核心技术,这主要是因为其在不受监督的学习、集群、分类和密度估计领域应用了集束化技术。有一种常客式方法是使用混合模型进行集束,混合模型被称为EM算法,通常对混合物模型的参数进行最大可能性估计。贝伊西亚的有限和无限高斯混合模型为所有变量得出点估计,并以整个估算的后背分布方式进行相关不确定性。本次调查的唯一目的是在Bayesia数学推断中,对概念和数学工具进行自足的介绍,以在随后各节中无缝地介绍其应用。然而,我们清楚地认识到我们无法涵盖该领域所有有用和有趣的结果,而且鉴于本次讨论的范围很小,例如,对Dirrichlet样本的生成进行分解模型和Polya Urn方法的分解分析。我们首先请读者参考Drichlet混合模型领域的文献,对有限和无限的高斯混合模型模型模型的自我推导,对相关领域进行非常严格的介绍。2010年,关于其历史、历史、历史、历史、历史、历史、历史和历史背景的一些精细的自我调查,主要包括:2010年的G。