MML clustering of multi-state, Poisson, von Mises circular and Gaussian distributions
MML clustering of multi-state, Poisson, von Mises circular and Gaussian distributions
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DOI：
10.1023/a:1008992619036
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发表时间：
2000-01-01
影响因子：
2.2
通讯作者：
Dowe, DL
中科院分区：
文献类型：
--
作者：
Wallace, CS;Dowe, DL
最小消息长度（MML）是一种不变的贝叶斯点估计技术，它也是统计上一致和有效的。我们提供了MML归纳推理的简要概述（Wallace C.S.和Boulton D. M. 1968. Computer Journal，11：185-194; Wallace C.S.和弗里曼公关1987. J.皇家统计学会（系列B），49：240-252;华莱士C.S.和Dowe D.L.（1999年）。计算机杂志），以及它如何同时具有信息论和贝叶斯解释。然后，我们概述了MML是如何用于统计参数估计，以及如何MML混合建模程序，Snob（华莱士C. S。和Boulton D. M. 1968. Computer Journal，11：185-194; Wallace C.S. 1986.在：第十九届澳大利亚计算机科学会议（ACSC-9），第8卷，莫纳什大学，澳大利亚，第页。357-366; Wallace C.S.和Dowe D.L. 1994年b。In：Zhang C.等（Eds.），第七届澳大利亚联合会议。智能World Scientific，新加坡，pp. 37-44.参见http：//www.csse.monash.edu.au/-dld/Snob.html）使用来自各种参数估计的消息长度以使其能够将参数估计与组分数目的选择和组分相对丰度的估计联合收割机组合。消息长度是（在一个常数内）理论的后验概率（不是后验密度）的对数。因此，MML理论也可以被认为是具有最高后验概率的理论。Snob目前假设变量在每个组成部分中不相关，并允许来自高斯，离散多类别（或多状态或多项），泊松和von Mises圆形分布以及缺失数据的多变量数据。此外，Snob可以进行完全参数化的混合建模，除了估计组件的数量，参数的相对丰度和组件参数之外，还可以估计潜在的类分配。我们还报告了扩展的Snob的数据具有连续的或空间的相关性之间的观察，或属性之间的相关性。
Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also statistically consistent and efficient. We provide a brief overview of MML inductive inference (Wallace C.S. and Boulton D.M. 1968. Computer Journal, 11: 185-194; Wallace C.S. and Freeman P.R. 1987. J. Royal Statistical Society (Series B), 49: 240-252; Wallace C.S. and Dowe D.L. (1999). Computer Journal), and how it has both an information-theoretic and a Bayesian interpretation. We then outline how MML is used for statistical parameter estimation, and how the MML mixture modelling program, Snob (Wallace C.S. and Boulton D.M. 1968. Computer Journal, 11: 185-194; Wallace C.S. 1986. In: Proceedings of the Nineteenth Australian Computer Science Conference (ACSC-9), Vol. 8, Monash University, Australia, pp. 357-366; Wallace C.S. and Dowe D.L. 1994b. In: Zhang C. et al. (Eds.), Proc. 7th Australian Joint Conf. on Artif. Intelligence. World Scientific, Singapore, pp. 37-44. See http://www.csse.monash.edu.au/-dld/Snob.html) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with selection of the number of components and estimation of the relative abundances of the components. The message length is (to within a constant) the logarithm of the posterior probability (not a posterior density) of the theory. So, the MML theory can also be regarded as the theory with the highest posterior probability. Snob currently assumes that variables are uncorrelated within each component, and permits multi-variate data from Gaussian, discrete multi-category (or multi-state or multinomial), Poisson and von Mises circular distributions, as well as missing data. Additionally, Snob can do fully-parameterised mixture modelling, estimating the latent class assignments in addition to estimating the number of components, the relative abundances of the parameters and the component parameters. We also report on extensions of Snob for data which has sequential or spatial correlations between observations, or correlations between attributes.