Parameter Estimation for Non-Gaussian Model-Based Clustering with High-Dimensional Data

大数据是现代数据和统计分析的重要问题。计算机可以存储大量数据;然而，准确和快速分析数据的方法并没有跟上现代存储技术的进步。在某些情况下，数据未经分析就被丢弃。大数据统计分析的改进将有利于处理大量数据的任何领域，例如生物科学（例如，基因组学）、金融和信息学、天文学、宇宙学和气候科学。我提出的研究将利用一种称为进化计算（EC）的计算机编程形式。EC使用的技术是从自然选择的生物进化理论中复制而来的。在生物学中，目标通常是产生尽可能多的健康后代，这些后代继续产生自己的健康后代。基因组的随机突变会使一些孩子比他们的父母更健康，或者更不健康。更健康的孩子更有可能生下健康的后代，因此他们的基因会遗传下去。在我的研究中，“适应度”的衡量标准是算法在聚类大数据方面搜索最佳解决方案的能力。（聚类涉及考虑链接数据点的底层结构，以便它们可以被放入正确的组中，或正确地标记，例如，将基因表达与癌症类型联系起来）。交叉和变异等技术是从生物学中复制而来的，用于“进化”算法，使其每次运行都更适合。 ** 根据拟议的研究，进化算法（EA）将被开发，作为几乎无处不在的期望最大化（EM）算法及其变体的替代方案，用于高斯和非高斯混合模型的聚类方法。将为混合因子分析器模型、混合方差伽马分布和混合方差伽马因子分析器模型开发EA。其他短期目标包括开发多个缩放方差伽马分布的混合物。这将带来惊人的建模灵活性，同时也保证了集群凸性-产生的组件是超立方体，因此衰减速率可以在每个维度上不同。将多尺度方差-伽玛分布混合模型推广到多尺度方差-伽玛因子分析器混合模型，以应用于高维数据。然后，将开发EA的混合物的多个缩放方差伽马分布和混合物的多个缩放方差伽马因子分析模型和研究交替的期望条件最大化算法的替代方案。

Big data is an important issue for modern data and statistical analysis. Computers can store huge amounts of data; however, methods to accurately and quickly analyze the data have not kept pace with improvements to modern storage technology. In some cases, data are discarded without being analyzed. Improved statistical analysis of big data will benefit any field dealing with massive amounts of data, such as biological sciences (e.g., genomics), finance and informatics, astronomy, cosmology, and climate science.******My proposed research will utilize a form of computer programming called Evolutionary Computation (EC). EC uses techniques copied from the biological theory of evolution by natural selection. In biology, the goal usually is to produce as many fit offspring as possible, who go on to produce their own fit offspring. Random mutations to the genome will make some children more fit, or less fit, than their parents. The fitter children are more likely to produce healthy offspring, so their genes get passed on. For my research, the measure of "fitness" used is how well the algorithm searches for optimum solutions with regard to clustering big data. (Clustering involves accounting for the underlying structure that links data points, so that they can be put into correct groups, or labelled correctly, e.g., linking gene expression to types of cancer.) Techniques such as cross-over and mutation are copied from biology, and are used to "evolve" the algorithm and make it fitter each time it runs. ******Under the proposed research, evolutionary algorithms (EAs) will be developed, as alternatives to the almost ubiquitous expectation-maximization (EM) algorithm and its variants, for Gaussian and non-Gaussian mixture model-based approaches to clustering. EAs will be developed for the mixture of factor analyzers model, the mixture of variance-gamma distributions, and the mixture of variance-gamma factor analyzers models. Other short term objectives include the development of a mixture of multiple scaled variance-gamma distributions. This will bring a phenomenal level of modelling flexibility, while also guaranteeing cluster convexity -- the resulting components are hypercubiods so that the rate of decay can differ in each dimension. The mixture of multiple scaled variance-gamma distributions model will be extended to the mixture of multiple scaled variance-gamma factor analyzers model, for application to high-dimensional data. EAs will then be developed for the mixture of multiple scaled variance-gamma distributions and mixture of multiple scaled variance-gamma factor analyzers models and investigated as alternatives to alternating expectation-conditional maximization algorithms.