Model-based learning on high-dimensional biological data

混合模型仍然是学习异构数据中隐藏聚类结构的最流行的方法。基于混合的聚类分析假设数据来自同质子种群的混合，其中聚类可以通过组件密度进行参数化建模。在基于模型的聚类（无监督）中，与基于模型的分类（半监督）相反，没有任何组标签信息可用于任何观察。概率混合模型聚类的优点以及这类模型的统计基础已经很好地建立起来。申请人研究项目的长期目标是为生物和临床数据集开发灵活的统计模型，以更深入地了解复杂的潜在过程。虽然不断开发灵活的模型，但仍然存在一些挑战。混合高斯分布仍然很流行，但在存在重尾、异常值等情况下表现不佳。申请人发表了多变量功率指数分布的混合，最近提出了多变量偏斜功率指数分布的混合。后一种混合可以是细峰或平峰，也可以是模型偏态。与最先进的竞争对手的严格比较显示出出色的聚类和分类性能，然而，这些混合物对于高维数据集仍然是过度参数化的。提出的研究将侧重于开发能够处理基于子空间聚类的高维数据的混合物，假设大多数数据存在于较低维子空间中，从而限制要估计的特定组件参数的数量。这将允许高度精简的模型，可以解释尾部权重，簇峰性和偏度。另一个重点将是在数据缺失时开发完全期望最大化（EM）方法的替代方案。这将通过观测值的边际密度方法来实现，该方法比全EM计算成本更低，并且不易受到随机缺失的严重违反的影响。当数据本质上是高维的并且存在缺失时，这种灵活性尤为重要。此外，在活动记录时间序列数据的激励下，混合模型将用于聚类具有变化点的时间序列。这些模型将以一种无监督、无测试的方式检测变化点，同时对观察结果进行聚类。这种方法将被扩展到协变量，以及具有变化点的多变量时间序列建模。所提出的工作代表了基于模型的多变量和时间序列数据聚类的重要一步。所提出的模型将能够解释变化的尾重，偏度，峰度，模型高维简洁，并解释计算效率的缺失。模型将通过用户友好的R软件包和顶级期刊提供。

Mixture models continue to be the most popular approach for learning hidden cluster structure in heterogenous data. Mixture-based cluster analysis assumes that data arise from a mixture of homogenous subpopulations where a cluster can be modeled parametrically via a component density. In model-based clustering (unsupervised) as opposed to model-based classification (semi-supervised), no group label information is available for any observations. Advantages of probabilistic mixture model clustering as well as the statistical grounding for such models is well established. The long term goal of the applicant's research program is to develop flexible statistical models for biological and clinical data sets to gain deeper insight into complex underlying processes. While flexible models continue to be developed, some challenges remain. Mixtures of Gaussian distributions remain popular but perform poorly in the presence of heavy tails, outliers, etc. The applicant has published on mixtures of multivariate power exponential distributions and recently proposed a mixture of multivariate skew power exponential distributions. These latter mixtures can be both leptokurtic or platykurtic, and model skewness. A rigorous comparison to state-of-the-art competitors showed excellent clustering and classification performance, however, these mixtures remain over-parametrized for high-dimensional datasets. The proposed research will focus on developing mixtures that can deal with high dimensional data based on subspace clustering assuming that most of the data exists in a lower dimensional subspace thereby limiting the number of component-specific parameters to be estimated. This will allow for highly parsimonious models that can account for tail weight, cluster peakedness, and skewness. Another focus will be to develop an alternative to a full expectation-maximization (EM) approach when the data has missingness. This will be done via a marginal density of observed values approach that is less computationally expensive than full EM and less susceptible to severe violations of missing at random. This flexibility is particularly important when the data are both high dimensional in nature and have missingness. Furthermore, motivated by actigraphy time series data, mixture models will be used to cluster time series with changepoints. These models will detect changepoints in an unsupervised, test-free, fashion while simultaneously clustering observations. This approach will be extended to account for covariates, as well as modeling multivariate time series with change points. The work proposed represents a major step forward in model-based clustering of multivariate and time series data. The proposed models will be able to account for varying tail weight, skewness, kurtosis, model high dimensions parsimoniously, and account for missingness computationally efficiently. Models will be made available via user friendly R packages and top tier journals.