Model-based learning on high-dimensional biological data

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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.